We apply three equilibrium selection techniques to study which equilibrium is selected in a hawk–dove game with a multiplicity of equilibria. By using a uniform-price auction as an illustrative example, we find that when the demand in the auction is low or intermediate, the tracing procedure method of Harsanyi and Selten (1988) and the quantal response method of McKelvey and Palfrey (1998) select the same equilibrium. When the demand is high, the tracing procedure method does not select any equilibrium, but the quantal response method still selects the same equilibrium as when the demand is low or intermediate. The robustness to strategic uncertainty method of Andersson, Argenton and Weibull (2014) selects two of the multiple equilibria irrespective of the demand size. We also analyze the impact of an increase in the minimum bid allowed by the auctioneer in the equilibrium selection.
{"title":"Equilibrium Selection in Hawk–Dove Games","authors":"Mario Blázquez de Paz, Nikita Koptyug","doi":"10.3390/g15010002","DOIUrl":"https://doi.org/10.3390/g15010002","url":null,"abstract":"We apply three equilibrium selection techniques to study which equilibrium is selected in a hawk–dove game with a multiplicity of equilibria. By using a uniform-price auction as an illustrative example, we find that when the demand in the auction is low or intermediate, the tracing procedure method of Harsanyi and Selten (1988) and the quantal response method of McKelvey and Palfrey (1998) select the same equilibrium. When the demand is high, the tracing procedure method does not select any equilibrium, but the quantal response method still selects the same equilibrium as when the demand is low or intermediate. The robustness to strategic uncertainty method of Andersson, Argenton and Weibull (2014) selects two of the multiple equilibria irrespective of the demand size. We also analyze the impact of an increase in the minimum bid allowed by the auctioneer in the equilibrium selection.","PeriodicalId":35065,"journal":{"name":"Games","volume":"6 5","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139130391","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 article, we investigate the relative performance of artificial neural networks and structural models of decision theory by training 69 artificial intelligence models on a dataset of 7080 human decisions in extensive form games. The objective is to compare the predictive power of AIs that use a representation of another agent’s decision-making process in order to improve their own performance during a strategic interaction. We use human game theory data for training and testing. Our findings hold implications for understanding how AIs can use constrained structural representations of other decision makers, a crucial aspect of our ‘Theory of Mind’. We show that key psychological features, such as the Weber–Fechner law for economics, are evident in our tests, that simple linear models are highly robust, and that being able to switch between different representations of another agent is a very effective strategy. Testing different models of AI-ToM paves the way for the development of learnable abstractions for reasoning about the mental states of ‘self’ and ‘other’, thereby providing further insights for fields such as social robotics, virtual assistants, and autonomous vehicles, and fostering more natural interactions between people and machines.
{"title":"Testing Game Theory of Mind Models for Artificial Intelligence","authors":"Michael S. Harré, Husam El-Tarifi","doi":"10.3390/g15010001","DOIUrl":"https://doi.org/10.3390/g15010001","url":null,"abstract":"In this article, we investigate the relative performance of artificial neural networks and structural models of decision theory by training 69 artificial intelligence models on a dataset of 7080 human decisions in extensive form games. The objective is to compare the predictive power of AIs that use a representation of another agent’s decision-making process in order to improve their own performance during a strategic interaction. We use human game theory data for training and testing. Our findings hold implications for understanding how AIs can use constrained structural representations of other decision makers, a crucial aspect of our ‘Theory of Mind’. We show that key psychological features, such as the Weber–Fechner law for economics, are evident in our tests, that simple linear models are highly robust, and that being able to switch between different representations of another agent is a very effective strategy. Testing different models of AI-ToM paves the way for the development of learnable abstractions for reasoning about the mental states of ‘self’ and ‘other’, thereby providing further insights for fields such as social robotics, virtual assistants, and autonomous vehicles, and fostering more natural interactions between people and machines.","PeriodicalId":35065,"journal":{"name":"Games","volume":"95 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139149253","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 study cooperation and coordination in a threshold public goods game with asymmetric players where players have different endowments ei, productivities pi, and rewards ri. In general, this game has a defective Nash equilibrium (NE), in which no one contributes, and multiple cooperative NEs, in which the group’s collective contribution equals the threshold. We then study how multiple dimensions of inequality influence people’s cooperation and coordination. We show that heterogeneity in eipi can promote cooperation in the sense that the existence condition of the defective NE becomes stricter. Furthermore, players with higher eipi are likely to contribute more at a cooperative NE in terms of collective contribution (i.e., absolute contribution multiplied by productivity).
在本文中，我们研究的是一个门槛公共产品博弈中的合作与协调问题，在这个博弈中，博弈者的禀赋 ei、生产率 pi 和回报 ri 都不对称。一般来说，这个博弈有一个有缺陷的纳什均衡（NE），即没有人做出贡献；也有多个合作的纳什均衡，即群体的集体贡献等于门槛值。然后，我们研究了不平等的多个维度如何影响人们的合作与协调。我们发现，eipi 的异质性可以促进合作，因为缺陷 NE 的存在条件变得更加严格。此外，就集体贡献（即绝对贡献乘以生产率）而言，eipi 越高的参与者越有可能在合作性 NE 上做出更多贡献。
{"title":"Cooperation and Coordination in Threshold Public Goods Games with Asymmetric Players","authors":"Xinmiao An, Yali Dong, Xiaomin Wang, Boyu Zhang","doi":"10.3390/g14060076","DOIUrl":"https://doi.org/10.3390/g14060076","url":null,"abstract":"In this paper, we study cooperation and coordination in a threshold public goods game with asymmetric players where players have different endowments ei, productivities pi, and rewards ri. In general, this game has a defective Nash equilibrium (NE), in which no one contributes, and multiple cooperative NEs, in which the group’s collective contribution equals the threshold. We then study how multiple dimensions of inequality influence people’s cooperation and coordination. We show that heterogeneity in eipi can promote cooperation in the sense that the existence condition of the defective NE becomes stricter. Furthermore, players with higher eipi are likely to contribute more at a cooperative NE in terms of collective contribution (i.e., absolute contribution multiplied by productivity).","PeriodicalId":35065,"journal":{"name":"Games","volume":"20 12","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138965752","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 describe the Factored Value MCTS Hybrid Cost-Max-Plus algorithm, a collection of decision-making algorithms (centralized, decentralized, and hybrid) for a multi-agent system in a collaborative setting that considers action costs. Our proposed algorithm is made up of two steps. In the first step, each agent searches for the best individual actions with the lowest cost using the Monte Carlo Tree Search (MCTS) algorithm. Each agent’s most promising activities are chosen and presented to the team. The Hybrid Cost Max-Plus method is utilized for joint action selection in the second step. The Hybrid Cost Max-Plus algorithm improves the well-known centralized and distributed Max-Plus algorithm by incorporating the cost of actions in agent interactions. The Max-Plus algorithm employed the Coordination Graph framework, which exploits agent dependencies to decompose the global payoff function as the sum of local terms. In terms of the number of agents and their interactions, the suggested Factored Value MCTS-Hybrid Cost-Max-Plus method is online, anytime, distributed, and scalable. Our contribution competes with state-of-the-art methodologies and algorithms by leveraging the locality of agent interactions for planning and acting utilizing MCTS and Max-Plus algorithms.
{"title":"Collaborative Cost Multi-Agent Decision-Making Algorithm with Factored-Value Monte Carlo Tree Search and Max-Plus","authors":"Nii-Emil Alexander-Reindorf, Paul Cotae","doi":"10.3390/g14060075","DOIUrl":"https://doi.org/10.3390/g14060075","url":null,"abstract":"In this paper, we describe the Factored Value MCTS Hybrid Cost-Max-Plus algorithm, a collection of decision-making algorithms (centralized, decentralized, and hybrid) for a multi-agent system in a collaborative setting that considers action costs. Our proposed algorithm is made up of two steps. In the first step, each agent searches for the best individual actions with the lowest cost using the Monte Carlo Tree Search (MCTS) algorithm. Each agent’s most promising activities are chosen and presented to the team. The Hybrid Cost Max-Plus method is utilized for joint action selection in the second step. The Hybrid Cost Max-Plus algorithm improves the well-known centralized and distributed Max-Plus algorithm by incorporating the cost of actions in agent interactions. The Max-Plus algorithm employed the Coordination Graph framework, which exploits agent dependencies to decompose the global payoff function as the sum of local terms. In terms of the number of agents and their interactions, the suggested Factored Value MCTS-Hybrid Cost-Max-Plus method is online, anytime, distributed, and scalable. Our contribution competes with state-of-the-art methodologies and algorithms by leveraging the locality of agent interactions for planning and acting utilizing MCTS and Max-Plus algorithms.","PeriodicalId":35065,"journal":{"name":"Games","volume":"30 25","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138966009","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}
Jonathan S. A. Merlevede, Benjamin Johnson, Jens Grossklags, Tom Holvoet
In recent years, several high-profile incidents have spurred research into games of timing. A framework emanating from the FlipIt model features two covert agents competing to control a single contested resource. In its basic form, the resource exists forever while generating value at a constant rate. As this research area evolves, attempts to introduce more economically realistic models have led to the application of various forms of economic discounting to the contested resource. This paper investigates the application of a two-parameter economic discounting method, called generalized hyperbolic discounting, and characterizes the game’s Nash equilibrium conditions. We prove that for agents discounting such that accumulated value generated by the resource diverges, equilibrium conditions are identical to those of non-discounting agents. The methodology presented in this paper generalizes the findings of several other studies and may be of independent interest when applying economic discounting to other models.
{"title":"Generalized Hyperbolic Discounting in Security Games of Timing","authors":"Jonathan S. A. Merlevede, Benjamin Johnson, Jens Grossklags, Tom Holvoet","doi":"10.3390/g14060074","DOIUrl":"https://doi.org/10.3390/g14060074","url":null,"abstract":"In recent years, several high-profile incidents have spurred research into games of timing. A framework emanating from the FlipIt model features two covert agents competing to control a single contested resource. In its basic form, the resource exists forever while generating value at a constant rate. As this research area evolves, attempts to introduce more economically realistic models have led to the application of various forms of economic discounting to the contested resource. This paper investigates the application of a two-parameter economic discounting method, called generalized hyperbolic discounting, and characterizes the game’s Nash equilibrium conditions. We prove that for agents discounting such that accumulated value generated by the resource diverges, equilibrium conditions are identical to those of non-discounting agents. The methodology presented in this paper generalizes the findings of several other studies and may be of independent interest when applying economic discounting to other models.","PeriodicalId":35065,"journal":{"name":"Games","volume":"70 ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139204010","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}
Poker is a game of skill, much like chess or go, but distinct as an incomplete information game. Substantial work has been done to understand human play in poker, as well as the optimal strategies in poker. Evolutionary game theory provides another avenue to study poker by considering overarching strategies, namely rational and random play. In this work, a population of poker playing agents is instantiated to play the preflop portion of Texas Hold’em poker, with learning and strategy revision occurring over the course of the simulation. This paper aims to investigate the influence of learning dynamics on dominant strategies in poker, an area that has yet to be investigated. Our findings show that rational play emerges as the dominant strategy when loss aversion is included in the learning model, not when winning and magnitude of win are of the only considerations. The implications of our findings extend to the modeling of sub-optimal human poker play and the development of optimal poker agents.
{"title":"Factors in Learning Dynamics Influencing Relative Strengths of Strategies in Poker Simulation","authors":"Aaron Foote, Maryam Gooyabadi, Nikhil Addleman","doi":"10.3390/g14060073","DOIUrl":"https://doi.org/10.3390/g14060073","url":null,"abstract":"Poker is a game of skill, much like chess or go, but distinct as an incomplete information game. Substantial work has been done to understand human play in poker, as well as the optimal strategies in poker. Evolutionary game theory provides another avenue to study poker by considering overarching strategies, namely rational and random play. In this work, a population of poker playing agents is instantiated to play the preflop portion of Texas Hold’em poker, with learning and strategy revision occurring over the course of the simulation. This paper aims to investigate the influence of learning dynamics on dominant strategies in poker, an area that has yet to be investigated. Our findings show that rational play emerges as the dominant strategy when loss aversion is included in the learning model, not when winning and magnitude of win are of the only considerations. The implications of our findings extend to the modeling of sub-optimal human poker play and the development of optimal poker agents.","PeriodicalId":35065,"journal":{"name":"Games","volume":"320 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139214469","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 investigate optimal delegation mechanisms in the presence of countervailing conflicts of interest in the context of principal–agent problems. We introduce two dimensions of conflict of interest—pandering incentives related to the outside option and project biases. We compare three delegation mechanisms: full delegation, veto-based delegation, and communication (no delegation). Contrary to conventional one-dimensional conflict models, our findings reveal a non-monotonic relationship between pandering incentives and bias. These conflicts counterbalance each other, resulting in a principal’s benefit from delegation not strictly decreasing with increased bias. Surprisingly, delegation to a biased agent can be advantageous in certain scenarios. This research sheds light on the complex dynamics of delegation mechanisms when confronted with countervailing conflicts of interest, offering insights into decision-making in principal–agent relationships.
{"title":"Countervailing Conflicts of Interest in Delegation Games","authors":"Saori Chiba, Kaiwen Leong","doi":"10.3390/g14060071","DOIUrl":"https://doi.org/10.3390/g14060071","url":null,"abstract":"In this paper, we investigate optimal delegation mechanisms in the presence of countervailing conflicts of interest in the context of principal–agent problems. We introduce two dimensions of conflict of interest—pandering incentives related to the outside option and project biases. We compare three delegation mechanisms: full delegation, veto-based delegation, and communication (no delegation). Contrary to conventional one-dimensional conflict models, our findings reveal a non-monotonic relationship between pandering incentives and bias. These conflicts counterbalance each other, resulting in a principal’s benefit from delegation not strictly decreasing with increased bias. Surprisingly, delegation to a biased agent can be advantageous in certain scenarios. This research sheds light on the complex dynamics of delegation mechanisms when confronted with countervailing conflicts of interest, offering insights into decision-making in principal–agent relationships.","PeriodicalId":35065,"journal":{"name":"Games","volume":"1 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2023-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139267728","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 analyze the location of final goods producers under spatial competition with strategic input price determination by firm-specific input suppliers when the final goods producers undertake complete outsourcing or bi-sourcing. Under complete outsourcing, the final goods producers locate closer as the distance between the input suppliers decreases, but the distance between the final goods producers may increase or decrease with the transportation costs of the consumers and the transportation costs between the input suppliers and the final goods producers depending on the distance between the input suppliers. The possibility of bi-sourcing reduces the benefit from saving the transportation costs between the input suppliers and the final goods producers, and creates effects which are opposite to those under complete outsourcing. Thus, our results differ significantly from the extant literature considering either no strategic input price determination or strategic input price determination under competition in the input market. We also discuss the implications on the profits, consumer surplus and welfare, and the implications of endogenous location choice of the input suppliers.
{"title":"Location of Firms and Outsourcing","authors":"Stefano Colombo, Arijit Mukherjee","doi":"10.3390/g14060070","DOIUrl":"https://doi.org/10.3390/g14060070","url":null,"abstract":"We analyze the location of final goods producers under spatial competition with strategic input price determination by firm-specific input suppliers when the final goods producers undertake complete outsourcing or bi-sourcing. Under complete outsourcing, the final goods producers locate closer as the distance between the input suppliers decreases, but the distance between the final goods producers may increase or decrease with the transportation costs of the consumers and the transportation costs between the input suppliers and the final goods producers depending on the distance between the input suppliers. The possibility of bi-sourcing reduces the benefit from saving the transportation costs between the input suppliers and the final goods producers, and creates effects which are opposite to those under complete outsourcing. Thus, our results differ significantly from the extant literature considering either no strategic input price determination or strategic input price determination under competition in the input market. We also discuss the implications on the profits, consumer surplus and welfare, and the implications of endogenous location choice of the input suppliers.","PeriodicalId":35065,"journal":{"name":"Games","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135927974","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 an agency model with adverse selection, we study how hidden interactions between agents affect the optimal contract. The principal employs two agents who learn their task environments through their involvement. The principal cannot observe the task environments. It is important to note that hidden interactions, such as acts of sabotage or help between the agents, have the potential to alter each other’s task environments. Our analysis encompasses two distinct organizational structures: competition and cooperation. Without hidden interactions, the competitive structure is optimal because the cooperative structure only provides the agents with more flexibility to collusively misrepresent their task environments. With hidden interactions, however, the cooperative structure induces the agents to help each other to improve the task environments while removing sabotaging incentives at no cost once collusion is deterred. As a result, the cooperative structure can be optimal in such a case. We discuss the link between production technology and organizational structure, finding that complementarity in production favors cooperative structures.
{"title":"Vertical Relationships with Hidden Interactions","authors":"Jaesoo Kim, Dongsoo Shin","doi":"10.3390/g14060069","DOIUrl":"https://doi.org/10.3390/g14060069","url":null,"abstract":"In an agency model with adverse selection, we study how hidden interactions between agents affect the optimal contract. The principal employs two agents who learn their task environments through their involvement. The principal cannot observe the task environments. It is important to note that hidden interactions, such as acts of sabotage or help between the agents, have the potential to alter each other’s task environments. Our analysis encompasses two distinct organizational structures: competition and cooperation. Without hidden interactions, the competitive structure is optimal because the cooperative structure only provides the agents with more flexibility to collusively misrepresent their task environments. With hidden interactions, however, the cooperative structure induces the agents to help each other to improve the task environments while removing sabotaging incentives at no cost once collusion is deterred. As a result, the cooperative structure can be optimal in such a case. We discuss the link between production technology and organizational structure, finding that complementarity in production favors cooperative structures.","PeriodicalId":35065,"journal":{"name":"Games","volume":"112 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135809542","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}
A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk {Xn,n=0,1,…} in the continuation region C:={1,2,…}, and the second player seeks to maximize the survival time in C. The process starts at X0=x>0 and the game ends the first time Xn≤0. An exact expression is derived for the value function, from which the optimal solution is obtained, and particular problems are solved explicitly.
{"title":"A Discrete-Time Homing Problem with Two Optimizers","authors":"Mario Lefebvre","doi":"10.3390/g14060068","DOIUrl":"https://doi.org/10.3390/g14060068","url":null,"abstract":"A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk {Xn,n=0,1,…} in the continuation region C:={1,2,…}, and the second player seeks to maximize the survival time in C. The process starts at X0=x>0 and the game ends the first time Xn≤0. An exact expression is derived for the value function, from which the optimal solution is obtained, and particular problems are solved explicitly.","PeriodicalId":35065,"journal":{"name":"Games","volume":"15 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136263981","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}
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