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on Game Theory |
| By: | Burkhard C. Schipper (Department of Economics, University of California Davis) |
| Abstract: | We provide an evolutionary foundation to evidence that in some situations humans maintain either optimistic or pessimistic attitudes towards uncertainty and are ignorant to relevant aspects of the environment. Players in strategic games face Knightian uncertainty about opponents' actions and maximize individually their Choquet expected utility with respect to neo-additive capacities (Chateauneuf, Eichberger, and Grant, 2007) allowing for both an optimistic or pessimistic attitude towards uncertainty as well as ignorance to strategic dependencies. An optimist (resp. pessimist) overweights good (resp. bad) outcomes. A complete ignorant never reacts to opponents' changes of actions. With qualifications we show that in finite populations optimistic (resp. pessimistic) complete ignorance is evolutionary stable and yields a strategic advantage in submodular (resp. supermodular) games with aggregate externalities. Moreover, this evolutionary stable preference leads to Walrasian behavior in these classes of games. |
| Keywords: | ambiguity, Knightian uncertainty, Choquet expected utility, neo-additive capacity, Hurwicz criterion, Maximin, Minimax, supermodularity, aggregative games, monotone comparative statics, playing the field, evolution of preferences |
| JEL: | C72 C73 D01 D43 D81 L13 |
| Date: | 2019–09–17 |
| URL: | http://d.repec.org/n?u=RePEc:cda:wpaper:334&r=all |
| By: | Trudeau, Christian; Vidal-Puga, Juan |
| Abstract: | We introduce a new family of cooperative games for which there is coincidence between the nucleolus and the Shapley value. These so-called clique games are such that agents are divided into cliques, with the value created by a coalition linearly increasing with the number of agents belonging to the same clique. Agents can belong to multiple cliques, but for a pair of cliques, at most a single agent belong to their intersection. Finally, if two agents do not belong to the same clique, there is at most one way to link the two agents through a chain of agents, with any two non-adjacent agents in the chain belonging to disjoint sets of cliques. We provide multiple examples for clique games. Graph-induced games, either when the graph indicates cooperation possibilities or impossibilities, provide us with opportunities to confirm existing results or discover new ones. A particular focus are the minimum cost spanning tree problems. Our result allows us to obtain new correspondence results between the nucleolus and the Shapley value, as well as other cost sharing methods for the minimum cost spanning tree problem. |
| Keywords: | nucleolus; Shapley value; clique; minimum cost spanning tree |
| JEL: | C71 |
| Date: | 2018–10–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:95999&r=all |
| By: | Encarnacion Algaba (Seville University); Rene van den Brink (Vrije Universiteit Amsterdam) |
| Abstract: | In this paper we focus on restrictions arising from the players belonging to some hierarchical structure that is represented by a digraph. Two of these models are the games with a permission structure and games under precedence constraints. In both cases, the hierarchy can be represented by a directed graph which restricts the possibilities of coalition formation. These two approaches led to two different type of solutions in the literature. The precedence power solutions for games under precedence constraints, are axiomatized with an axiom that applies a network power measure to the precedence constraint. We will show that something similar can be done for games with a permission structure, and obtain a class of permission power solutions. This class contains the (conjunctive) permission value. With this we have two classes of solutions for games with a hierarchy, one based on permission structures and another based on precedence constraints, that are characterized by similar axioms. Moreover, the solutions are linked with network power measures. |
| Keywords: | Cooperative transferable utility game, permission structures, precedence constraints, Shapley value, hierarchical solution, power measures |
| JEL: | C71 |
| Date: | 2019–08–09 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20190064&r=all |
| By: | Hino, Yoshifumi |
| Abstract: | We consider an infinitely repeated prisoner's dilemma under costly monitoring. If a player observes his opponent, then he pays an observation cost and knows the action chosen by his opponent. If a player does not observe his opponent, he cannot obtain any information about his opponent's action. Furthermore, no player can statistically identify the observational decision of his opponent. We prove efficiency without any signals. Then, we extend the idea with a public randomization device and we present a folk theorem for a sufficiently small observation cost when players are sufficiently patient. |
| Keywords: | Costly observation; Efficiency; Folk theorem; Prisoner's dilemma |
| JEL: | C72 C73 D82 |
| Date: | 2018–12–10 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:96010&r=all |
| By: | Loretta Mastroeni; Maurizio Naldi; Pierluigi Vellucci |
| Abstract: | Investors usually resort to financial advisors to improve their investment process until the point of complete delegation on investment decisions. Surely, financial advice is potentially a correcting factor in investment decisions but, in the past, the media and regulators blamed biased advisors for manipulating the expectations of naive investors. In order to give an analytic formulation of the problem, we present an Agent-Based Model formed by individual investors and a financial advisor. We parametrize the games by considering a compromise for the financial advisor (between a sufficient reward by bank and to keep his/her reputation), and a compromise for the customers (between the desired return and the proposed return by advisor). Then we obtain the Nash equilibria and the best response functions of the resulting game. We also describe the parameter regions in which these points result acceptable equilibria and the greediness/naivety of the customers emerge naturally from the model. Finally, we focus on the efficiency of the best Nash equilibrium. |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1909.06759&r=all |
| By: | Mark Armstrong; John Vickers |
| Abstract: | We study mixed-strategy equilibrium pricing in oligopoly settings where con-sumers vary in the set of suppliers they consider for their purchase-some being captive to a particular firm, some consider two particular firms, and so on. In the case of "nested reach" we find equilibria, unlike those in more standard models, in which firms are ranked in terms of the prices they might charge. We character-ize equilibria in the three-firm case, and contrast them with equilibria in the parallel model with capacity constraints. A theme of the analysis is how patterns of consumer interaction with firms matter for competitive outcomes. |
| JEL: | C72 D43 D83 L15 |
| Date: | 2018–12–05 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:864&r=all |
| By: | David Ronayne; David P. Myatt |
| Abstract: | We propose a two-stage replacement for established “clearinghouse" or “captive and shopper" pricing models: second-stage retail prices are constrained by first-stage list prices. In contrast to the mixed-strategy equilibria of single-stage games, a unique profile of distinct prices is supported by the play of pure strategies along the equilibrium path, and so we predict stable price dispersion. We find novel results in applications to models of sales, product prominence, advertising, and consumer search. |
| Keywords: | price dispersion, clearinghouse models, prominence, advertising, buyer search |
| Date: | 2019–06–20 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:873&r=all |
| By: | Dirk Bergemann (Cowles Foundation, Yale University); Tibor Heumann (Dept. of Economics, Yale University); Stephen Morris (Dept. of Economics, Princeton University) |
| Abstract: | We consider demand function competition with a ï¬ nite number of agents and private information. We show that any degree of market power can arise in the unique equilibrium under an information structure that is arbitrarily close to complete information. In particular, regardless of the number of agents and the correlation of payoff shocks, market power may be arbitrarily close to zero (so we obtain the competitive outcome) or arbitrarily large (so there is no trade in equilibrium). By contrast, price volatility is always less than the variance of the aggregate shock across all information structures. |
| Keywords: | Demand Function Competition, Supply Function Competition, Price Impact, Market Power, Incomplete Information, Price Volatility |
| JEL: | C72 D43 D44 D83 G12 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2200&r=all |
| By: | Choo, Lawrence; Kaplan, Todd R.; Zhou, Xiaoyu |
| Abstract: | In this paper, we seek to determine if auctions can be used to select players according to their level-k types. To do so, we embed auctions into the p-beauty contest game. We find that by using different designs, we can get the auction winners to be either the lower level-k types or the higher level-k types. In particular, when the value of winning the auction is increasing in the level-k types of all the players, higher level-k players bid higher. When the value of winning the auction is decreasing in the level-k types of all the players, the lower level-k players bid higher. Taken together, our experiment confirms that we can use auctions to select players by their level-k types. This shows that auctions can allow an economic designer to affect the outcome of a game through the selection of level-k types entering to play the game. |
| Keywords: | p-beauty contest game, level-k, auctions, mechanism design. |
| JEL: | C72 C90 D44 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:95987&r=all |
| By: | Johannes Johnen; David Ronayne |
| Abstract: | We study a canonical model of simultaneous price competition between firms that sell a homogeneous good to consumers who are characterized by the number of prices they are exogenously aware of. This setting subsumes many used in the literature over the past several decades. Our result shows that there is a unique equilibrium if and only if there exist some consumers who are aware of exactly two prices. The equilibrium we derive is in symmetric mixed strategies. Further¬more, when there are no consumers aware of exactly two prices, we show there is an uncountable-infinity of asymmetric equilibria in addition to the symmetric equilibrium. Our result shows that the paradigm generically produces a unique equilibrium; that the commonly-sought symmetric equilibrium is robust; and that the asymmetric equilibria are knife-edge phenomena. |
| Keywords: | price competition; price dispersion; unique equilibrium |
| JEL: | D43 L11 |
| Date: | 2019–07–26 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:874&r=all |
| By: | Anwesha Banerjee (Aix-Marseille Univ, CNRS, EHESS, Ecole Centrale, AMSE, Marseille, France.); Nicolas Gravel (Centre de Sciences Humaines, 2, Dr APJ Abdul Kalam Road, 11 0011 Delhi, India. & Aix-Marseille Univ., CNRS, EHESS, Centrale Marseille, AMSE) |
| Abstract: | This paper examines how voluntary contributions to a public good are affected by the contributors' heterogeneity in beliefs about the uncertain impact of their contributions. It assumes that contributors have Savagian preferences that are represented by a two-state-dependent expected utility function and different beliefs about the benefit that will result from the sum of their contributions. We establish general comparative statics results regarding the effect of specific changes in the distribution of beliefs on the (unique) Nash equilibrium provision of the public good, under certain conditions imposed on the preferences. We specifically show that the equilibrium public good provision is increasing with respect to both first and second order stochastic dominance changes in the distribution of beliefs. Hence, increasing the contributors' optimism about the uncertain benefit of their contributions increases aggregate public good provision provision, as does any homogenization of these beliefs around their mean. |
| Keywords: | voluntary provision, public good, uncertainty, beliefs, optimism, consensus |
| JEL: | C72 H41 |
| Date: | 2019–09 |
| URL: | http://d.repec.org/n?u=RePEc:aim:wpaimx:1923&r=all |
| By: | Nakao, Keisuke |
| Abstract: | How do belligerents choose and change their military strategies during war? How do these strategies shape war? To address these questions, we develop a random-walk model of war, where two belligerents fight over "forts" across periods. The random walk represents a battlefront, which moves as the war evolves, resulting in the occupation of more forts for the winning side and less forts for the losing side. Unlike existing models, ours allows the belligerents to choose an action out of moving forward, inflicting costs, and surrender in every battle. We found that equilibrium strategies are monotonic with respect to the walk---a belligerent will punish its opponent if it is sufficiently advantageous and surrender if it is too disadvantageous. Accordingly, the punishment strategy can function to shorten the war. Moreover, a severer punishment tends to make the war even shorter. |
| Keywords: | gambler's ruin, military strategy, random walk |
| JEL: | C73 D74 F51 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:96071&r=all |
| By: | Matthew Weinberg (The Ohio State University, Department of); Gloria Sheu (US Department of Justice, Antitrust Division); Nathan Miller (Georgetown University) |
| Abstract: | We examine an infinitely-repeated game of oligopoly price leadership in which each period one firm, the market leader, proposes a supermarkup over Nash-Bertrand prices. The supermarkup is chosen to maximize the leader's profit subject to all firms' incentive compatibility constraints (ICCs). We provide conditions under which the equilibrium supermarkup can be recovered from aggregate data on price and quantities. We apply the model to the U.S. beer industry over 2005-2011 and estimate that ABI and MillerCoors implemented supermarkups of $\$0.60$ in the wake of the 2008 Miller/Coors merger. Counterfactual simulations demonstrate an ICC binds, as profit is greater with even higher supermarkups. We use the implied equality constraint to jointly identify a discount factor and the antitrust risk, the remaining structural parameters. We then explore the coordinated effects of ABI's acquisition of Grupo Modelo. Without divestitures, the merger would have relaxed ICCs, resulting in substantially higher prices. Finally, we return to the Miller/Coors merger. For many parameter values, no supermarkup satisfies ICCs without the merger. Thus, the merger may have be pivotal in generating the observed price leadership behavior. |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:red:sed019:1210&r=all |
| By: | Denis Claude (LEDi - Laboratoire d'Economie de Dijon [Dijon] - UB - Université de Bourgogne - UBFC - Université Bourgogne Franche-Comté [COMUE]); Mabel Tidball (CEE-M - Centre d'Economie de l'Environnement - Montpellier - FRE2010 - INRA - Institut National de la Recherche Agronomique - UM - Université de Montpellier - CNRS - Centre National de la Recherche Scientifique - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier) |
| Abstract: | This paper explores the link between upstream input pricing and downstream strategic delegation decisions. It complements earlier contributions by studying how environmental emissions and tax payments alter the incentives business owners have to divert their managers from profit maximization in favor of sales revenue generation. Two scenarios are compared depending on whether the upstream supplier precommits to a fixed input price or adopts a flexible price strategy. Corresponding Subgame-Perfect Nash-Equilibria are characterized and elements of comparative statics analysis are presented. The analysis confirms that previous results—showing that a price precommitment makes the upstream supplier better off and downstream firms worse off—carry over to situations in which production generates pollution. |
| Keywords: | Managerial incentives,Vertical relations,Delegation,Precommitment,Externality |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-02283174&r=all |
| By: | Danková, Katarína; Morita, Hodaka; Servátka, Maroš; Zhang, Le |
| Abstract: | How does job assignment affect fairness concerns between coworkers? We experimentally examine agents’ horizontal fairness concerns in a three-person ultimatum game in which all agents are asked to complete a general knowledge quiz before being assigned to a high productivity or low productivity position. Job positions differ in the stakes that are available to be split between the principal and the agent. We disentangle two possible channels through which job assignment impacts fairness concerns, wage differences and the principal’s intentions, by comparing cases in which the job assignment is determined randomly or by the principal. The knowledge quiz signifies the distinction between the two cases as it provides a basis on which the principal can make the assignment decision. We find that the principal’s intentions, combined with the associated wage differences, significantly impact fairness concerns of the agents assigned to the lower productivity position, but wage differences themselves do not. We also find that better-performing agents assigned by the principal to the lower productivity position exhibit significant fairness concerns toward their peers. We discuss managerial implications of our findings. |
| Keywords: | job assignment, fairness concerns, experiment, ultimatum game, wage differences, intentions |
| JEL: | C91 C92 J31 J71 |
| Date: | 2019–09–06 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:95918&r=all |