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on Game Theory |
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Issue of 2013‒06‒04
twelve papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Rene van den Brink (VU University Amsterdam); Jean-Jacques Herings (Maastricht University); Gerard van der Laan (VU University Amsterdam); Dolf Talman (Tilburg University) |
| Abstract: | In the literature various models of games with restricted cooperation can be found. In those models, instead of allowing for all subsets of the set of players to form, it is assumed that the set of feasible coalitions is a proper subset of the power set of the set of players. In this paper we consider such sets of feasible coalitions that follow from a permission structure on the set of players, in which players need permission to cooperate with other players. We assume the permission structure to be an oriented tree. This means that there is one player at the top of the permission structure and for every other player there is a unique directed path from the top player to this player. We introduce a new solution for these games based on the idea of the Average Tree value for cycle-free communication graph games. We provide two axiomatizations for this new value and compare it with the conjunctive permission value. |
| Keywords: | TU game, restricted cooperation, permission structure, Shapley value, Average Tree value, axiomatization |
| JEL: | C71 |
| Date: | 2012–01–24 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:2013023&r=gth |
| By: | Olivier Compte (Paris School of Economics); Andrew Postlewaite (Department of Economics, University of Pennsylvania) |
| Abstract: | Much of the repeated game literature is concerned with proving Folk Theorems. The logic of the exercise is to specify a particular game, and to explore for that game specification whether any given feasible (and individually rational) value vector can be an equilibrium outcome for some strategies when agents are sufficiently patient. A game specification includes a description of what agents observe at each stage. This is done by defining a monitoring structure, that is, a collection of probability distributions over the signals players receive (one distribution for each action profile players may play). Although this is simply meant to capture the fact that players don’t directly observe the actions chosen by others, constructed equilibria often depend on players precisely knowing these distributions, somewhat unrealistic in most problems of interest. We revisit the classic Folk Theorem for games with imperfect public monitoring, asking that incentive conditions hold not only for a precisely defined monitoring structure, but also for a ball of monitoring structures containing it. We show that efficiency and incentives are no longer compatible. |
| Keywords: | Repeated games, folk theorem, robustness |
| JEL: | C72 C73 |
| Date: | 2013–01–03 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:13-022&r=gth |
| By: | Hannu Salonen (Department of Economics, University of Turku, Finland) |
| Abstract: | We study games with utilitarian preferences: the sum of individual utility functions is a generalized ordinal potential for the game. It turns out that generically, any finite game with a potential, ordinal potential, or generalized ordinal potential is better reply equivalent to a game with utilitarian preferences. It follows that generically, finite games with a generalized ordinal potential are better reply equivalent to potential games. For infinite games we show that a continuous game has a continuous ordinal potential, iff there is a better reply equivalent continuous game with utilitarian preferences. For such games we show that best reply improvement paths can be used to approximate equilibria arbitrarily closely. |
| Keywords: | potential games, best reply equivalence, utilitarian preferences |
| JEL: | C72 D43 |
| Date: | 2013–05 |
| URL: | http://d.repec.org/n?u=RePEc:tkk:dpaper:dp85&r=gth |
| By: | Hyndman, Kyle; Terracol, Antoine; Vaksmann, Jonathan |
| Abstract: | In this paper, we use experimental data to study players' stability in normal-form games where subjects have to report beliefs and to choose actions. Subjects saw each of 12 games four times in a regular or isomorphic form spread over two days without feedback. We document a high degree of stability within the same (strategically equivalent) game, although time and changes in the presentation of the game do lead to less stability. To look at stability across different games, we adopt the level-k theory, and show that stability of both beliefs and actions is significantly lower. Finally, we estimate a structural model in which players either apply a consistent level of reasoning across strategically different games, or reasoning levels change from game to game. Our results show that approximately 30% of subjects apply a consistent level of reasoning across the 12 games, but that they assign a low level of sophistication to their opponent. The remaining 70% apply different levels of reasoning to different games. |
| Keywords: | Game theory, Beliefs, Stability, Level-$k$ thinking |
| JEL: | C72 C91 D83 |
| Date: | 2013–05–23 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:47221&r=gth |
| By: | H Peyton Young; H.H. Nax; M.N. Burton-Chellew; S.A. West |
| Abstract: | Many interactive environments can be represented as games, but they are so large and complex that individual players are in the dark about what others are doing and how their own payoffs are affected. This paper analyzes learning behavior in such 'black box' environments, where players' only source of information is their own history of actions taken and payoffs received. Specifically we study repeated public goods games, where players must decide how much to contribute at each stage, but they do not know how much others have contributed or how others' contributions affect their own payoffs. We identify two key features of the players' learning dynamics. First, if a player's realized payoff increases he is less inclined to change his strategy, whereas if his realized payoff decreases he is more inclined to change his strategy. Second, if increasing his own contribution results in higher payoffs he will tend to increase his contribution still further, whereas the reverse holds if an increase in contribution leads to lower payoffs. These two effects are clearly present when players have no information about the game; moreover they are still present even when players have full information. Convergence to Nash equilibrium occurs at about the same rate in both situations. |
| Keywords: | Learning, information, public goods games |
| JEL: | C70 C73 C91 D83 H41 |
| Date: | 2013–04–23 |
| URL: | http://d.repec.org/n?u=RePEc:oxf:wpaper:653&r=gth |
| By: | DEHEZ, Pierre (Université catholique de Louvain, CORE, B-1348 Louvain-la-Neuve, Belgium); POUKENS, SOPHIE (Université catholique de Louvain, Belgium) |
| Abstract: | We consider the problem of specifying Fair, Reasonable And Non-Discriminatory agreements faced by standard-setting organizations. Along with Layne-Farrar, Padilla and Schmalensee (2007), we model the problem as a cooperative game with transferable utility, allowing for patents to be weak in the sense that they have substitutes. Assuming that a value has been assigned to weak patents, we obtain a formula for the Shapley value that gives an insight into what FRAND agreements should look like. |
| Keywords: | patent licensing, Shapley value, core |
| Date: | 2013–05–06 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2013012&r=gth |
| By: | HOUGAARD, Jens L. (University of Copenhagen); moreno-ternero, JUAN D. (Universidad Pablo de Olavide, Spain and Université catholique de Louvain, CORE, Belgium); OSTERDAL, Lars P. (University of Southern Denmark) |
| Abstract: | We consider the problem of assigning agents to slots on a line, where only one agent can be served at a slot and each agent prefers to be served as close as possible to his target. Our focus is on utilitarian methods, i.e., those that minimize the total gap between targets and assigned slots. We first consider deterministic assignment of agents to slots, and provide a direct method for testing if a given deterministic assignment is utilitarian. We then consider probabilistic assignment of agents to slots, and make use of the previous method to propose a utilitarian modification of the classic random priority method to solve this class of problems. We also provide some logical relations in our setting among standard axioms in the literature on assignment problems. |
| Keywords: | probabilistic assignment, random priority, utilitarianism, sd-efficiency, bottleneck |
| JEL: | C78 D61 D63 |
| Date: | 2013–05–06 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2013015&r=gth |
| By: | Marco Pelliccia (Department of Economics, Mathematics & Statistics, Birkbeck) |
| Abstract: | We investigate the impact of network structures describing reciprocal influence-relationships between agents on their perceived ambiguity. We argue that, under specific assumptions, the potential complexity of the link-structures creates extra uncertainty or ambiguity over the "right" probability distribution to consider. This result affects the optimal equilibrium structures which arise in a dynamic game where the agents/nodes strategically rewire their links to minimize the perceived uncertainty. The model could explain specific network dynamics observed in markets with asymmetric or not perfect information on the partners' outcomes. For instance, we propose an interpretation of the dynamic of the European Interbank Market structure before and after the recent financial crisis. |
| Keywords: | Ambiguity, Network, Interbank Market |
| JEL: | D85 D81 D82 G21 |
| Date: | 2013–02 |
| URL: | http://d.repec.org/n?u=RePEc:bbk:bbkefp:1303&r=gth |
| By: | Hassan Benchekroun; Farnaz Taherkhani |
| Abstract: | We consider a game of abatement of a transboundary pollutant. We use a time-consistent Shapley value allocation of the cost of pollution reduction, and study the sensitivity of such an allocation to countries' adaptation to pollution. A country's adaptation to pollution is captured by a change in its damage function. We show that if there is a reduction in the damage cost of one country only, this can harm the other countries. Some countries may end up worse o¤ even in the case where all countries experience a uniform decrease in their damage from pollution. An important policy implication of our analysis is that the Shapley value approach to the allocation of abatement costs doesn't necessarily provide the right incentives for all players to act on reducing pollution damage. We determine conditions under which a uniform fall in all countries'pollution damage benefits all countries. |
| Keywords: | adaptation, Shapley value, transboundary pollution, climate change, time-consistency |
| JEL: | C71 Q2 Q54 Q55 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:mtl:montec:03-2013&r=gth |
| By: | Massimo Morelli; Dominic Rohner |
| Abstract: | This paper highlights the importance of natural resource concentration and ethnic group regional concentration for ethnic conflict. A new type of bargaining failure due to multiple types of potential conflicts (and hence multiple threat points) is identified. The theory predicts war to be more likely when resource and group concentration are high, and the empirical analysis, both at the country level and at the ethnic group level, confirms the essential role of geographic concentration variables for civil war. |
| Keywords: | Natural Resources; Civil War; Conflict; Secession; Bargaining Failure |
| JEL: | C72 D74 Q34 |
| Date: | 2013–05 |
| URL: | http://d.repec.org/n?u=RePEc:lau:crdeep:13.08&r=gth |
| By: | Giacomo Bonanno (Department of Economics, University of California Davis) |
| Abstract: | This is the first draft of a chapter in a planned book on the Prisoner’s Dilemma, edited by Martin Peterson, to be published by Cambridge University Press. It discusses the nature of the conditionals involved in deliberation, taking the Prisoner's Dilemma game as point of departure. |
| Keywords: | Prisoner's Dilemma, deliberation, belief, subjunctive conditional, indicative conditional, counterfactual, causal decision theory |
| JEL: | C7 |
| Date: | 2013–05–17 |
| URL: | http://d.repec.org/n?u=RePEc:cda:wpaper:13-7&r=gth |
| By: | Xiao, Erte; Tan, Fangfang |
| Abstract: | Punishment can lose its legitimacy if the enforcer can profit from delivering punishment. We use a controlled laboratory experiment to examine how justification can combat profit-seeking punishment and promote the legitimacy of punishment. In a one-shot sender-receiver game, an independent third party can punish the sender upon seeing whether the sender has told the truth. Most third parties punish the senders regardless of how the senders behave when they can profit from punishment. However, majority third parties punish the sender if and only if the sender lies when they have to provide explanations for their punishment decisions. Our data also suggests that senders are more likely to perceive punishment as legitimate and behave honestly when they know the enforcer has to justify their punishment decisions. Our findings suggest that justification requirement plays an important role in building efficient punishment institutions. |
| Keywords: | third-party punishment, justification, sender-receiver game, experiment |
| JEL: | C72 C92 D63 D83 |
| Date: | 2013–05–22 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:47154&r=gth |