In security games, the defender often has to predict the attacker’s behavior based on some observed attack data. However, a clever attacker can intentionally change its behavior to mislead the defender’s learning, leading to an ineffective defense strategy. This paper investigates the attacker’s imitative behavior deception under uncertainty, in which the attacker mimics a (deceptive) Quantal Response behavior model by consistently playing according to a certain parameter value of that model, given that it is uncertain about the defender’s actual learning outcome. We have three main contributions. First, we introduce a new maximin-based algorithm to compute a robust attacker deception decision under uncertainty, given the defender is unaware of the attacker deception. Our polynomial algorithm is built via characterizing the decomposability of the attacker deception space as well optimal deception behavior of the attacker against the worst case of uncertainty. Second, we propose a new counter-deception algorithm to tackle the attacker’s deception. We theoretically show that there is a universal optimal defense solution, regardless of any private knowledge the defender has about the relation between their learning outcome and the attacker deception choice. Third, we conduct extensive experiments in various security game settings, demonstrating the effectiveness of our proposed counter-deception algorithms to handle the attacker manipulation.
{"title":"A Complete Analysis on the Risk of Using Quantal Response: When Attacker Maliciously Changes Behavior under Uncertainty","authors":"T. Nguyen, A. Yadav","doi":"10.3390/g13060081","DOIUrl":"https://doi.org/10.3390/g13060081","url":null,"abstract":"In security games, the defender often has to predict the attacker’s behavior based on some observed attack data. However, a clever attacker can intentionally change its behavior to mislead the defender’s learning, leading to an ineffective defense strategy. This paper investigates the attacker’s imitative behavior deception under uncertainty, in which the attacker mimics a (deceptive) Quantal Response behavior model by consistently playing according to a certain parameter value of that model, given that it is uncertain about the defender’s actual learning outcome. We have three main contributions. First, we introduce a new maximin-based algorithm to compute a robust attacker deception decision under uncertainty, given the defender is unaware of the attacker deception. Our polynomial algorithm is built via characterizing the decomposability of the attacker deception space as well optimal deception behavior of the attacker against the worst case of uncertainty. Second, we propose a new counter-deception algorithm to tackle the attacker’s deception. We theoretically show that there is a universal optimal defense solution, regardless of any private knowledge the defender has about the relation between their learning outcome and the attacker deception choice. Third, we conduct extensive experiments in various security game settings, demonstrating the effectiveness of our proposed counter-deception algorithms to handle the attacker manipulation.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"81"},"PeriodicalIF":0.9,"publicationDate":"2022-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46142499","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This article is an overview of recent progress on a theory of games, whose payoffs are probability distributions rather than real numbers, and which have their equilibria defined and computed over a (suitably restricted yet dense) set of distributions. While the classical method of defining game models with real-valued utility functions has proven strikingly successful in many domains, some use cases from the security area revealed shortcomings of the classical real-valued game models. These issues motivated the use of probability distributions as a more complex object to express revenues. The resulting class of games displays a variety of phenomena not encountered in classical games, such as games that have continuous payoff functions but still no equilibrium, or games that are zero-sum but for which fictitious play does not converge. We discuss suitable restrictions of how such games should be defined to allow the definition of equilibria, and show the notion of a lexicographic Nash equilibrium, as a proposed solution concept in this generalized class of games.
{"title":"Games over Probability Distributions Revisited: New Equilibrium Models and Refinements","authors":"S. Rass, Sandra König, S. Schauer","doi":"10.3390/g13060080","DOIUrl":"https://doi.org/10.3390/g13060080","url":null,"abstract":"This article is an overview of recent progress on a theory of games, whose payoffs are probability distributions rather than real numbers, and which have their equilibria defined and computed over a (suitably restricted yet dense) set of distributions. While the classical method of defining game models with real-valued utility functions has proven strikingly successful in many domains, some use cases from the security area revealed shortcomings of the classical real-valued game models. These issues motivated the use of probability distributions as a more complex object to express revenues. The resulting class of games displays a variety of phenomena not encountered in classical games, such as games that have continuous payoff functions but still no equilibrium, or games that are zero-sum but for which fictitious play does not converge. We discuss suitable restrictions of how such games should be defined to allow the definition of equilibria, and show the notion of a lexicographic Nash equilibrium, as a proposed solution concept in this generalized class of games.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"80"},"PeriodicalIF":0.9,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44174203","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present the results of an experiment conducted in Italy on trusting behaviour. Our subjects participated in a trust game and filled in a questionnaire on trust and trustworthiness based on the attitudinal questions reported in the European Value Survey. The aims of the research are twofold. Firstly, using the experimental dataset, we construct two measures of trustworthiness among all recipients in the experiment, one based on the questionnaires’ answers and another based on the strategy method. We then compare the ex-ante behavioural decision to trust (before participants are allocated to a group) with the ex-post decision to trust (after participants are allocated to a group and trustors are informed of the level of trustworthiness of all the recipients who have been randomly allocated to each group). Our main finding is that trust strongly varies once the information is disclosed to trustors. The effect on trust is greater when the strategy method is used. Secondly, we compare the behavioural measure of trust with the attitudinal measures of trust and trustworthiness and find that there is only a weak correlation between the two measures, thus confirming, for the Italian case, similar findings in country-based studies on trust.
{"title":"An Experimental Investigation of Trusting Behaviour","authors":"Clelia Mazzoni, Patrizia Sbriglia","doi":"10.3390/g13060079","DOIUrl":"https://doi.org/10.3390/g13060079","url":null,"abstract":"In this paper, we present the results of an experiment conducted in Italy on trusting behaviour. Our subjects participated in a trust game and filled in a questionnaire on trust and trustworthiness based on the attitudinal questions reported in the European Value Survey. The aims of the research are twofold. Firstly, using the experimental dataset, we construct two measures of trustworthiness among all recipients in the experiment, one based on the questionnaires’ answers and another based on the strategy method. We then compare the ex-ante behavioural decision to trust (before participants are allocated to a group) with the ex-post decision to trust (after participants are allocated to a group and trustors are informed of the level of trustworthiness of all the recipients who have been randomly allocated to each group). Our main finding is that trust strongly varies once the information is disclosed to trustors. The effect on trust is greater when the strategy method is used. Secondly, we compare the behavioural measure of trust with the attitudinal measures of trust and trustworthiness and find that there is only a weak correlation between the two measures, thus confirming, for the Italian case, similar findings in country-based studies on trust.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"79"},"PeriodicalIF":0.9,"publicationDate":"2022-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44583430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let Φn be the set of the binary strategy-proof social choice functions referred to a group of n voters who are allowed to declare indifference between the alternatives. We provide a recursive way to obtain the set Φn+1 from the set Φn. Computing the cardinalities |Φn| presents difficulties as the computation of the Dedekind numbers. The latter give the analogous number of social choice functions when only strict preferences are admitted. A comparison is given for the known values. Based on our results, we present a graphical description of the binary strategy-proof social choice functions in the case of three voters.
{"title":"A Note on Binary Strategy-Proof Social Choice Functions","authors":"A. Basile, A. Simone, C. Tarantino","doi":"10.3390/g13060078","DOIUrl":"https://doi.org/10.3390/g13060078","url":null,"abstract":"Let Φn be the set of the binary strategy-proof social choice functions referred to a group of n voters who are allowed to declare indifference between the alternatives. We provide a recursive way to obtain the set Φn+1 from the set Φn. Computing the cardinalities |Φn| presents difficulties as the computation of the Dedekind numbers. The latter give the analogous number of social choice functions when only strict preferences are admitted. A comparison is given for the known values. Based on our results, we present a graphical description of the binary strategy-proof social choice functions in the case of three voters.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"78"},"PeriodicalIF":0.9,"publicationDate":"2022-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44289456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies how the cost of delay and voting order affect agents’ decisions in a unanimity voting mechanism. Specifically, we consider two-voter conclaves with commonly known preferences over two alternatives, the cost of delay, and the following novelty: each voter has a subjective deadline—a moment in time when he/she prefers immediate agreement on any alternative, rather than future agreement on his/her most-preferred alternative. Our key finding shows that patience is not necessarily a main attribute of strategic advantage. When the first voter is the same at every stage, this voter will obtain his/her preferred alternative, even if he/she is the least patient one. However, this first movement advantage disappears when agents alternate as the first voter of each stage: in this case, the most patient voter always wins.
{"title":"The Unanimity Rule under a Two-Agent Fixed Sequential Order Voting","authors":"M. Bannikova, José-Manuel Giménez-Gómez","doi":"10.3390/g13060077","DOIUrl":"https://doi.org/10.3390/g13060077","url":null,"abstract":"This paper studies how the cost of delay and voting order affect agents’ decisions in a unanimity voting mechanism. Specifically, we consider two-voter conclaves with commonly known preferences over two alternatives, the cost of delay, and the following novelty: each voter has a subjective deadline—a moment in time when he/she prefers immediate agreement on any alternative, rather than future agreement on his/her most-preferred alternative. Our key finding shows that patience is not necessarily a main attribute of strategic advantage. When the first voter is the same at every stage, this voter will obtain his/her preferred alternative, even if he/she is the least patient one. However, this first movement advantage disappears when agents alternate as the first voter of each stage: in this case, the most patient voter always wins.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"77"},"PeriodicalIF":0.9,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42742109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Alessandra F. Lütz, M. Amaral, I. Braga, L. Wardil
The stag-hunt game is a prototype for social contracts. Adopting a new and better social contract is usually challenging because the current one is already well established and stable due to sanctions imposed on non-conforming members. Thus, how does a population shift from the current social contract to a better one? In other words, how can a social system leave a locally optimum configuration to achieve a globally optimum state? Here, we investigate the effect of promoting diversity on the evolution of social contracts. We consider group-structured populations where individuals play the stag-hunt game in all groups. We model the diversity incentive as a snowdrift game played in a single focus group where the individual is more prone to adopting a deviant norm. We show that a moderate diversity incentive is sufficient to change the system dynamics, driving the population over the stag-hunt invasion barrier that prevents the global optimum being reached. Thus, an initial fraction of adopters of the new, better norm can drive the system toward the optimum social contract. If the diversity incentive is not too large, the better social contract is the new equilibrium and remains stable even if the incentive is turned off. However, if the incentive is large, the population is trapped in a mixed equilibrium and the better social norm can only be reached if the incentive is turned off after the equilibrium is reached. The results are obtained using Monte Carlo simulations and analytical approximation methods.
{"title":"Invasion of Optimal Social Contracts","authors":"Alessandra F. Lütz, M. Amaral, I. Braga, L. Wardil","doi":"10.3390/g14030042","DOIUrl":"https://doi.org/10.3390/g14030042","url":null,"abstract":"The stag-hunt game is a prototype for social contracts. Adopting a new and better social contract is usually challenging because the current one is already well established and stable due to sanctions imposed on non-conforming members. Thus, how does a population shift from the current social contract to a better one? In other words, how can a social system leave a locally optimum configuration to achieve a globally optimum state? Here, we investigate the effect of promoting diversity on the evolution of social contracts. We consider group-structured populations where individuals play the stag-hunt game in all groups. We model the diversity incentive as a snowdrift game played in a single focus group where the individual is more prone to adopting a deviant norm. We show that a moderate diversity incentive is sufficient to change the system dynamics, driving the population over the stag-hunt invasion barrier that prevents the global optimum being reached. Thus, an initial fraction of adopters of the new, better norm can drive the system toward the optimum social contract. If the diversity incentive is not too large, the better social contract is the new equilibrium and remains stable even if the incentive is turned off. However, if the incentive is large, the population is trapped in a mixed equilibrium and the better social norm can only be reached if the incentive is turned off after the equilibrium is reached. The results are obtained using Monte Carlo simulations and analytical approximation methods.","PeriodicalId":35065,"journal":{"name":"Games","volume":"14 1","pages":"42"},"PeriodicalIF":0.9,"publicationDate":"2022-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48845986","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The black box method was developed as an "asocial control" to allow for payoff-based learning while eliminating social responses in repeated public goods games. Players are told they must decide how many virtual coins they want to input into a virtual black box that will provide uncertain returns. However, in truth, they are playing with each other in a repeated social game. By "black boxing" the game's social aspects and payoff structure, the method creates a population of self-interested but ignorant or confused individuals that must learn the game's payoffs. This low-information environment, stripped of social concerns, provides an alternative, empirically derived null hypothesis for testing social behaviours, as opposed to the theoretical predictions of rational self-interested agents (Homo economicus). However, a potential problem is that participants can unwittingly affect the learning of other participants. Here, we test a solution to this problem in a range of public goods games by making participants interact, unknowingly, with simulated players ("computerised black box"). We find no significant differences in rates of learning between the original and the computerised black box, therefore either method can be used to investigate learning in games. These results, along with the fact that simulated agents can be programmed to behave in different ways, mean that the computerised black box has great potential for complementing studies of how individuals and groups learn under different environments in social dilemmas.
{"title":"The Black Box as a Control for Payoff-Based Learning in Economic Games.","authors":"Maxwell N Burton-Chellew, Stuart A West","doi":"10.3390/g13060076","DOIUrl":"10.3390/g13060076","url":null,"abstract":"<p><p>The black box method was developed as an \"asocial control\" to allow for payoff-based learning while eliminating social responses in repeated public goods games. Players are told they must decide how many virtual coins they want to input into a virtual black box that will provide uncertain returns. However, in truth, they are playing with each other in a repeated social game. By \"black boxing\" the game's social aspects and payoff structure, the method creates a population of self-interested but ignorant or confused individuals that must learn the game's payoffs. This low-information environment, stripped of social concerns, provides an alternative, empirically derived null hypothesis for testing social behaviours, as opposed to the theoretical predictions of rational self-interested agents (<i>Homo economicus</i>). However, a potential problem is that participants can unwittingly affect the learning of other participants. Here, we test a solution to this problem in a range of public goods games by making participants interact, unknowingly, with simulated players (\"computerised black box\"). We find no significant differences in rates of learning between the original and the computerised black box, therefore either method can be used to investigate learning in games. These results, along with the fact that simulated agents can be programmed to behave in different ways, mean that the computerised black box has great potential for complementing studies of how individuals and groups learn under different environments in social dilemmas.</p>","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 6","pages":"76"},"PeriodicalIF":0.6,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7614088/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10583103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider the problem of allocating heterogeneous objects to agents with money, where the number of agents exceeds that of objects. Each agent can receive at most one object, and some objects may remain unallocated. A bundle is a pair consisting of an object and a payment. An agent’s preference over bundles may not be quasi-linear, which exhibits income effects or reflects borrowing costs. We investigate the class of rules satisfying one of the central properties of fairness in the literature, egalitarian-equivalence, together with the other desirable properties. We propose (i) a novel class of rules that we call the independent second-prices rules with variable constraints and (ii) a novel condition on constraints that we call respecting the valuation coincidence. Then, we establish that the independent second-prices rule with variable constraints that respects the valuation coincidence is the only rule satisfying egalitarian-equivalence, strategy-proofness, individual rationality, and no subsidy for losers. Our characterization result implies that in the case of three or more agents, there are few opportunities for agents to receive objects under a rule satisfying egalitarian-equivalence and the other desirable properties, which highlights the strong tension between egalitarian-equivalence and efficiency. In contrast, in the case of two agents and a single object, egalitarian-equivalence is compatible with efficiency.
{"title":"Egalitarian-Equivalence and Strategy-Proofness in the Object Allocation Problem with Non-Quasi-Linear Preferences","authors":"Hiroki Shinozaki","doi":"10.3390/g13060075","DOIUrl":"https://doi.org/10.3390/g13060075","url":null,"abstract":"We consider the problem of allocating heterogeneous objects to agents with money, where the number of agents exceeds that of objects. Each agent can receive at most one object, and some objects may remain unallocated. A bundle is a pair consisting of an object and a payment. An agent’s preference over bundles may not be quasi-linear, which exhibits income effects or reflects borrowing costs. We investigate the class of rules satisfying one of the central properties of fairness in the literature, egalitarian-equivalence, together with the other desirable properties. We propose (i) a novel class of rules that we call the independent second-prices rules with variable constraints and (ii) a novel condition on constraints that we call respecting the valuation coincidence. Then, we establish that the independent second-prices rule with variable constraints that respects the valuation coincidence is the only rule satisfying egalitarian-equivalence, strategy-proofness, individual rationality, and no subsidy for losers. Our characterization result implies that in the case of three or more agents, there are few opportunities for agents to receive objects under a rule satisfying egalitarian-equivalence and the other desirable properties, which highlights the strong tension between egalitarian-equivalence and efficiency. In contrast, in the case of two agents and a single object, egalitarian-equivalence is compatible with efficiency.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"75"},"PeriodicalIF":0.9,"publicationDate":"2022-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44790813","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We experimentally investigated the effects of the possibility of taking in the dictator game and the choices of passive players between the dictator game and the taking game on the distribution decisions of active players. Our main findings support our hypothesis: when the dictator game is not exogenously given but chosen by the receivers (or passive players), this makes them accountable, which leads to less giving by dictators. We also conducted an online survey to gain further insights about our experimental results. Survey participants predicted most of the observed behavior in the experiment and explained the factors that might have driven the predicted behavior using reasoning similar to ours. Our results provide a new perspective for the dependence of giving in the dictator game on contextual factors.
{"title":"Endogenous Game Choice and Giving Behavior in Distribution Games","authors":"Emin Karagözoğlu, Elif Tosun","doi":"10.3390/g13060074","DOIUrl":"https://doi.org/10.3390/g13060074","url":null,"abstract":"We experimentally investigated the effects of the possibility of taking in the dictator game and the choices of passive players between the dictator game and the taking game on the distribution decisions of active players. Our main findings support our hypothesis: when the dictator game is not exogenously given but chosen by the receivers (or passive players), this makes them accountable, which leads to less giving by dictators. We also conducted an online survey to gain further insights about our experimental results. Survey participants predicted most of the observed behavior in the experiment and explained the factors that might have driven the predicted behavior using reasoning similar to ours. Our results provide a new perspective for the dependence of giving in the dictator game on contextual factors.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"74"},"PeriodicalIF":0.9,"publicationDate":"2022-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42812670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Revision game is a very recent advance in dynamic game theory and it can be used to analyze the trading in the pre-opening stock market. In such games, players prepare actions that will be implemented at a given deadline, before which they may have opportunities to revise actions. For the first time, we study the role of the deadline in revision games, which is the core component that distinguishes revision games from classic games. We introduce the deadline distribution into revision game model and characterize the sufficient and necessary condition for players’ strategies to constitute an equilibrium. The equilibrium strategy with respect to the deadline uncertainty is given by a simple differential equation set. Governed by this differential equation set, players initially fully cooperate, and the cooperation level decreases as time progresses. The uncertainty has a great impact on players’ behavior. As the uncertainty increases, players become more risk averse, in the sense that they prefer lower mutual cooperation rate rather than higher payoff with higher uncertainty. Specifically, they will not stay in full cooperation for a long time, while after they deviate from the full cooperation, they adjust their plans more slowly and cautiously. The deadline uncertainty can improve the competition and avoid collusion in games, which could be utilized for auction design and pre-opening stock market regulations.
{"title":"Characterizing Agent Behavior in Revision Games with Uncertain Deadline","authors":"Zhuohan Wang, Dong Hao","doi":"10.3390/g13060073","DOIUrl":"https://doi.org/10.3390/g13060073","url":null,"abstract":"Revision game is a very recent advance in dynamic game theory and it can be used to analyze the trading in the pre-opening stock market. In such games, players prepare actions that will be implemented at a given deadline, before which they may have opportunities to revise actions. For the first time, we study the role of the deadline in revision games, which is the core component that distinguishes revision games from classic games. We introduce the deadline distribution into revision game model and characterize the sufficient and necessary condition for players’ strategies to constitute an equilibrium. The equilibrium strategy with respect to the deadline uncertainty is given by a simple differential equation set. Governed by this differential equation set, players initially fully cooperate, and the cooperation level decreases as time progresses. The uncertainty has a great impact on players’ behavior. As the uncertainty increases, players become more risk averse, in the sense that they prefer lower mutual cooperation rate rather than higher payoff with higher uncertainty. Specifically, they will not stay in full cooperation for a long time, while after they deviate from the full cooperation, they adjust their plans more slowly and cautiously. The deadline uncertainty can improve the competition and avoid collusion in games, which could be utilized for auction design and pre-opening stock market regulations.","PeriodicalId":35065,"journal":{"name":"Games","volume":"13 1","pages":"73"},"PeriodicalIF":0.9,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49204948","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：