We consider mean-field contribution games, where players in a team choose some effort levels at each time period and the aggregate reward for the team depends on the aggregate cumulative performance of all the players. Each player aims to maximize the expected reward of her own share subject to her cost of effort. To reduce the free-rider issue, we propose some relative performance criteria (RPC), based on which the reward is redistributed to each player. We are interested in those RPCs that implement the optimal solution for the corresponding centralized problem, and we call such RPC an optimal one. That is, the expected payoff of each player under the equilibrium associated with an optimal RPC is as large as the value induced by the corresponding problem where players completely cooperate. We first analyze a one-period model with homogeneous players and obtain natural RPCs of different forms. Then, we generalize these results to a multiperiod model in discrete time. Next, we investigate a two-layer mean-field game. The top layer is an interteam game (team-wise competition), in which the reward of a team is impacted by the relative achievement of the team with respect to other teams; the bottom layer is an intrateam contribution game where an RPC is implemented for reward redistribution among team members. We establish the existence of equilibria for the two-layer game and characterize the intrateam optimal RPC. Finally, we extend the (one-layer) results of optimal RPCs to the continuous-time setup as well as to the case with heterogenous players.
{"title":"Optimal Relative Performance Criteria in Mean Field Contribution Games","authors":"Zhou Zhou","doi":"10.2139/ssrn.3742584","DOIUrl":"https://doi.org/10.2139/ssrn.3742584","url":null,"abstract":"We consider mean-field contribution games, where players in a team choose some effort levels at each time period and the aggregate reward for the team depends on the aggregate cumulative performance of all the players. Each player aims to maximize the expected reward of her own share subject to her cost of effort. To reduce the free-rider issue, we propose some relative performance criteria (RPC), based on which the reward is redistributed to each player. We are interested in those RPCs that implement the optimal solution for the corresponding centralized problem, and we call such RPC an optimal one. That is, the expected payoff of each player under the equilibrium associated with an optimal RPC is as large as the value induced by the corresponding problem where players completely cooperate. We first analyze a one-period model with homogeneous players and obtain natural RPCs of different forms. Then, we generalize these results to a multiperiod model in discrete time. Next, we investigate a two-layer mean-field game. The top layer is an interteam game (team-wise competition), in which the reward of a team is impacted by the relative achievement of the team with respect to other teams; the bottom layer is an intrateam contribution game where an RPC is implemented for reward redistribution among team members. We establish the existence of equilibria for the two-layer game and characterize the intrateam optimal RPC. Finally, we extend the (one-layer) results of optimal RPCs to the continuous-time setup as well as to the case with heterogenous players.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130575806","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 some Bayesian games, payoff-relevant states are influenced by unobserved player- or game-level heterogeneity that also also effects strategic decisions directly. Ignoring such endogeneity in empirical analysis leads to erroneous inference of structural parameters and policy implications. We introduce a control-function approach for estimating discrete Bayesian games with such endogeneity. We apply the method to analyze an entry game of deploying 4G-LTE technology by major U.S. cellphone service providers, taking existing network deployment in the focal market and current deployment in neighboring markets as endogenous. Using lagged demographics of neighboring markets as instruments, we find that a hypothetical T-Mobile and Sprint merger would reduce 4G-LTE deployment across local markets. Moreover, the entry of a fourth national provider, enabled by a partial divestiture of the merger’s assets, would not completely offset its negative impact on market entries and the population served. We also find that ignoring endogeneity in network deployment skews the policy implications by underpredicting the merger’s negative impacts on market entry.
{"title":"Endogeneity in Entry Games: U.S. Cellphone Service Deployment","authors":"Zhongjian Lin, Xun Tang, Mo Xiao","doi":"10.2139/ssrn.3741805","DOIUrl":"https://doi.org/10.2139/ssrn.3741805","url":null,"abstract":"In some Bayesian games, payoff-relevant states are influenced by unobserved player- or game-level heterogeneity that also also effects strategic decisions directly. Ignoring such endogeneity in empirical analysis leads to erroneous inference of structural parameters and policy implications. We introduce a control-function approach for estimating discrete Bayesian games with such endogeneity. We apply the method to analyze an entry game of deploying 4G-LTE technology by major U.S. cellphone service providers, taking existing network deployment in the focal market and current deployment in neighboring markets as endogenous. Using lagged demographics of neighboring markets as instruments, we find that a hypothetical T-Mobile and Sprint merger would reduce 4G-LTE deployment across local markets. Moreover, the entry of a fourth national provider, enabled by a partial divestiture of the merger’s assets, would not completely offset its negative impact on market entries and the population served. We also find that ignoring endogeneity in network deployment skews the policy implications by underpredicting the merger’s negative impacts on market entry.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127342823","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 paper studies when efficient allocations are implementable via coalition-proof mechanisms. When ambiguous mechanisms are allowed and agents are maxmin expected utility maximizers, we prove that all efficient allocations are implementable via interim coalition incentive compatible mechanisms if and only if the prior distribution of agents’ types satisfies the Coalition Beliefs Determine Preferences (CBDP) property. When the CBDP property holds, these mechanisms can be designed to satisfy additional conditions of interim coalition rationality, interim ambiguity insurance, and ex-post budget balance. When ambiguous mechanisms are not allowed, under every prior, there exists an efficient allocation that is not implementable via interim coalition incentive compatible simple mechanisms. Thus, the paper sheds light on how coalition-proofness may be achieved by engineering ambiguity in mechanism rules.
{"title":"Coalition-proof Ambiguous Mechanism","authors":"Huiyi Guo","doi":"10.2139/ssrn.3726822","DOIUrl":"https://doi.org/10.2139/ssrn.3726822","url":null,"abstract":"The paper studies when efficient allocations are implementable via coalition-proof mechanisms. When ambiguous mechanisms are allowed and agents are maxmin expected utility maximizers, we prove that all efficient allocations are implementable via interim coalition incentive compatible mechanisms if and only if the prior distribution of agents’ types satisfies the Coalition Beliefs Determine Preferences (CBDP) property. When the CBDP property holds, these mechanisms can be designed to satisfy additional conditions of interim coalition rationality, interim ambiguity insurance, and ex-post budget balance. When ambiguous mechanisms are not allowed, under every prior, there exists an efficient allocation that is not implementable via interim coalition incentive compatible simple mechanisms. Thus, the paper sheds light on how coalition-proofness may be achieved by engineering ambiguity in mechanism rules.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129453254","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}
I study, both empirically and theoretically, the economic and financial consequences of corporate lobbying. Firms lobby politicians to increase their share of government contracts, but political competition creates firm-level risk, inflating their cost of capital and reducing their incentive to invest in research and development (R&D). I document an annual 6%–8% return premium for stocks of high-lobbying firms, which compensates investors for political risk. An estimated model in which firms can lobby and innovate and investors are risk averse replicates key features of corporate lobbying in the US, including the well-established paradox that lobbying contributions are small relative to the policies at stake. The model predicts that if investors ceased seeking compensation for political risk, R&D investment would increase by 6% and the innovation rate by 0.4 percentage points. The risk-premium costs of lobbying are quantitatively and economically important even if the resources “wasted” on lobbying are objectively small.
{"title":"Follow the Money","authors":"M. Grotteria","doi":"10.2139/ssrn.3281201","DOIUrl":"https://doi.org/10.2139/ssrn.3281201","url":null,"abstract":"\u0000 I study, both empirically and theoretically, the economic and financial consequences of corporate lobbying. Firms lobby politicians to increase their share of government contracts, but political competition creates firm-level risk, inflating their cost of capital and reducing their incentive to invest in research and development (R&D). I document an annual 6%–8% return premium for stocks of high-lobbying firms, which compensates investors for political risk. An estimated model in which firms can lobby and innovate and investors are risk averse replicates key features of corporate lobbying in the US, including the well-established paradox that lobbying contributions are small relative to the policies at stake. The model predicts that if investors ceased seeking compensation for political risk, R&D investment would increase by 6% and the innovation rate by 0.4 percentage points. The risk-premium costs of lobbying are quantitatively and economically important even if the resources “wasted” on lobbying are objectively small.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123596266","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 2012, Brazilian public universities were mandated to use affirmative action policies for candidates from racial and income minorities. We show that the policy makes the students’ affirmative action status a strategic choice and may reject high-achieving minority students while admitting low-achieving majority students. Empirical data shows evidence consistent with this type of unfairness in more than 49 percent of the programs. We propose a selection criterion and an incentive-compatible mechanism that, for a wider range of similar problems and the one in Brazil in particular, is fair and removes any gain from strategizing over the privileges claimed. (JEL I23, O15, I28, J15, D82, H52)
{"title":"College Admission with Multidimensional Privileges: The Brazilian Affirmative Action Case","authors":"Orhan Aygun, Inácio Bó","doi":"10.2139/ssrn.3071751","DOIUrl":"https://doi.org/10.2139/ssrn.3071751","url":null,"abstract":"In 2012, Brazilian public universities were mandated to use affirmative action policies for candidates from racial and income minorities. We show that the policy makes the students’ affirmative action status a strategic choice and may reject high-achieving minority students while admitting low-achieving majority students. Empirical data shows evidence consistent with this type of unfairness in more than 49 percent of the programs. We propose a selection criterion and an incentive-compatible mechanism that, for a wider range of similar problems and the one in Brazil in particular, is fair and removes any gain from strategizing over the privileges claimed. (JEL I23, O15, I28, J15, D82, H52)","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124010774","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 balanced transferable utility game (N, v) has a stable core if its core is externally stable, that is, if each imputation that is not in the core is dominated by some core element. Given two payoff allocations x and y, we say that x outvotes y via some coalition S of a feasible set if x dominates y via S and x allocates at least v(T) to any feasible T that is not contained in S. It turns out that outvoting is transitive and the set M of maximal elements with respect to outvoting coincides with the core if and only if the game has a stable core. By applying the duality theorem of linear programming twice, it is shown that M coincides with the core if and only if a certain nested balancedness condition holds. Thus, it can be checked in finitely many steps whether a balanced game has a stable core. We say that the game has a super-stable core if each payoff vector that allocates less than v(S) to some coalition S is dominated by some core element and prove that core super-stability is equivalent to vital extendability, requiring that each vital coalition is extendable.
{"title":"Characterization of TU Games with Stable Cores by Nested Balancedness","authors":"M. Grabisch, Peter Sudhölter","doi":"10.2139/ssrn.3627087","DOIUrl":"https://doi.org/10.2139/ssrn.3627087","url":null,"abstract":"A balanced transferable utility game (N, v) has a stable core if its core is externally stable, that is, if each imputation that is not in the core is dominated by some core element. Given two payoff allocations x and y, we say that x outvotes y via some coalition S of a feasible set if x dominates y via S and x allocates at least v(T) to any feasible T that is not contained in S. It turns out that outvoting is transitive and the set M of maximal elements with respect to outvoting coincides with the core if and only if the game has a stable core. By applying the duality theorem of linear programming twice, it is shown that M coincides with the core if and only if a certain nested balancedness condition holds. Thus, it can be checked in finitely many steps whether a balanced game has a stable core. We say that the game has a super-stable core if each payoff vector that allocates less than v(S) to some coalition S is dominated by some core element and prove that core super-stability is equivalent to vital extendability, requiring that each vital coalition is extendable.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132808443","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 work, we study the assortment planning games in which multiple retailers interact in the market. Each retailer owns some of the products and their goal is to select a subset of products, i.e., an assortment to o er to the customers so as to maximize their expected revenue. The purchase behavior of the customer is assumed to follow the Markov chain choice model. We consider two types of assortment games under the Markov chain choice model - a competitive game and a cooperative game. In the assortment competition game, we show that there always exists a pure-strategy Nash equilibrium and such equilibrium can be found in polynomial time. We also identify an easy-to-check condition for the uniqueness of the Nash equilibrium. Then we analyze the equilibrium outcome on the assortments and the payoffs of this competition game, and compare the outcome with that in a monopolistic setting and a central planner setting. We show that under the assortment competition game, each retailer will o er a broader assortment in the equilibrium, which could include products that are not pro table in the monopolistic or the central planner setting, and it will eventually lead to a decrease of revenue for each player. Furthermore, we show that the price-of-anarchy and the price-of-stability of the game can be arbitrarily large. Motivated by these results, we further consider the assortment cooperation game under the Markov chain choice model, in which retailers are allowed to form coalitions. We consider two settings of cooperative games distinguished by how players presume other players' behavior. Interestingly, we find that when the players take a pessimistic view regarding the behavior of other players, there is incentive for all the players to form a grand coalition and there exists an allocation of the total revenue that makes the coalition stable (exists a core to the game). However, when the players take an optimistic view regarding the behavior of other players, a stable coalition may not exist.
{"title":"Competitive and Cooperative Assortment Games under Markov Chain Choice Model","authors":"K. Nip, Changjun Wang, Zizhuo Wang","doi":"10.2139/ssrn.3607722","DOIUrl":"https://doi.org/10.2139/ssrn.3607722","url":null,"abstract":"In this work, we study the assortment planning games in which multiple retailers interact in the market. Each retailer owns some of the products and their goal is to select a subset of products, i.e., an assortment to o er to the customers so as to maximize their expected revenue. The purchase behavior of the customer is assumed to follow the Markov chain choice model. We consider two types of assortment games under the Markov chain choice model - a competitive game and a cooperative game. \u0000 \u0000In the assortment competition game, we show that there always exists a pure-strategy Nash equilibrium and such equilibrium can be found in polynomial time. We also identify an easy-to-check condition for the uniqueness of the Nash equilibrium. Then we analyze the equilibrium outcome on the assortments and the payoffs of this competition game, and compare the outcome with that in a monopolistic setting and a central planner setting. We show that under the assortment competition game, each retailer will o er a broader assortment in the equilibrium, which could include products that are not pro table in the monopolistic or the central planner setting, and it will eventually lead to a decrease of revenue for each player. Furthermore, we show that the price-of-anarchy and the price-of-stability of the game can be arbitrarily large. Motivated by these results, we further consider the assortment cooperation game under the Markov chain choice model, in which retailers are allowed to form coalitions. We consider two settings of cooperative games distinguished by how players presume other players' behavior. Interestingly, we find that when the players take a pessimistic view regarding the behavior of other players, there is incentive for all the players to form a grand coalition and there exists an allocation of the total revenue that makes the coalition stable (exists a core to the game). However, when the players take an optimistic view regarding the behavior of other players, a stable coalition may not exist.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114032633","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 develop screening models of final offer arbitration (FOA) in which the uninformed party makes a demand to the informed party. We consider models in which settlement occurs before and after the submission of binding offers, and in each we analyze costly discovery. Our results are compared to conventional arbitration (CA) which may viewed as a litigation model. Overall, the incentive to invoke discovery is stronger in FOA than in CA, due in part, to informational rents often present in FOA, but not in CA. Moreover, submitted proposals under FOA contain information which raise the benefit of invoking discovery.
{"title":"Discovery in a Screening Model of Final Offer Arbitration","authors":"A. Farmer, Paul Pecorino","doi":"10.2139/ssrn.3606498","DOIUrl":"https://doi.org/10.2139/ssrn.3606498","url":null,"abstract":"We develop screening models of final offer arbitration (FOA) in which the uninformed party makes a demand to the informed party. We consider models in which settlement occurs before and after the submission of binding offers, and in each we analyze costly discovery. Our results are compared to conventional arbitration (CA) which may viewed as a litigation model. Overall, the incentive to invoke discovery is stronger in FOA than in CA, due in part, to informational rents often present in FOA, but not in CA. Moreover, submitted proposals under FOA contain information which raise the benefit of invoking discovery.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117030977","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 general markets with adverse selection in which symmetric firms supply (potentially multiple) products to privately-informed consumers and compete with price schedules. I show that a basic price cap regulation, in which the price caps are endogenously determined by firms, alongside the possibility of firms to react to price cuts a la Wilson (1977), discourages risk selection over efficient allocations, and therefore, equilibrium exists in every market. Moreover, I demonstrate that in the markets that are considerably more general than the stylised Rothschild and Stiglitz (1976) insurance market, firms earn zero profits in equilibrium, and every equilibrium allocation is efficient.
{"title":"Efficient Price Competition in Markets with Adverse Selection","authors":"Anastasios Dosis","doi":"10.2139/ssrn.3572800","DOIUrl":"https://doi.org/10.2139/ssrn.3572800","url":null,"abstract":"This paper studies general markets with adverse selection in which symmetric firms supply (potentially multiple) products to privately-informed consumers and compete with price schedules. I show that a basic price cap regulation, in which the price caps are endogenously determined by firms, alongside the possibility of firms to react to price cuts a la Wilson (1977), discourages risk selection over efficient allocations, and therefore, equilibrium exists in every market. Moreover, I demonstrate that in the markets that are considerably more general than the stylised Rothschild and Stiglitz (1976) insurance market, firms earn zero profits in equilibrium, and every equilibrium allocation is efficient.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116623244","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}
Strategic complements are well understood for normal form games, but less so for extensive form games. There is some evidence that extensive form games with strategic complementarities are a very restrictive class of games (Echenique (2004)). We study necessary and sufficient conditions for strategic complements (defined as increasing best responses) in two stage, 2x2 games. We find that the restrictiveness imposed by quasisupermodularity and single crossing property is particularly severe, in the sense that the set of games in which payoffs satisfy these conditions has measure zero. Payoffs with these conditions require the player to be indifferent between their actions in two of the four subgames in stage two, eliminating any strategic role for their actions in these two subgames. In contrast, the set of games that exhibit strategic complements (increasing best responses) has infinite measure. This enlarges the scope of strategic complements in two stage, 2x2 games (and provides a basis for possibly greater scope in more general games). The set of subgame perfect Nash equilibria in the larger class of games continues to remain a nonempty, complete lattice. The results are easy to apply, and are robust to including dual payoff conditions and adding a third player. Examples with several motivations are included.
{"title":"Dynamic Strategic Complements in Two Stage, 2x2 Games","authors":"Yue Feng, Tarun Sabarwal","doi":"10.2139/ssrn.3320646","DOIUrl":"https://doi.org/10.2139/ssrn.3320646","url":null,"abstract":"Strategic complements are well understood for normal form games, but less so for extensive form games. There is some evidence that extensive form games with strategic complementarities are a very restrictive class of games (Echenique (2004)). We study necessary and sufficient conditions for strategic complements (defined as increasing best responses) in two stage, 2x2 games. We find that the restrictiveness imposed by quasisupermodularity and single crossing property is particularly severe, in the sense that the set of games in which payoffs satisfy these conditions has measure zero. Payoffs with these conditions require the player to be indifferent between their actions in two of the four subgames in stage two, eliminating any strategic role for their actions in these two subgames. In contrast, the set of games that exhibit strategic complements (increasing best responses) has infinite measure. This enlarges the scope of strategic complements in two stage, 2x2 games (and provides a basis for possibly greater scope in more general games). The set of subgame perfect Nash equilibria in the larger class of games continues to remain a nonempty, complete lattice. The results are easy to apply, and are robust to including dual payoff conditions and adding a third player. Examples with several motivations are included.","PeriodicalId":393761,"journal":{"name":"ERN: Other Game Theory & Bargaining Theory (Topic)","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126621361","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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