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on Game Theory |
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Issue of 2011‒05‒30
eleven papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Normann, Hans-Theo; Wallace, Brian |
| Abstract: | Cooperation in prisoner's dilemma games can usually be sustained only if the game has an infinite horizon. We analyze to what extent the theoretically crucial distinction of finite vs. infinite-horizon games is reflected in the outcomes of a prisoner's dilemma experiment. We compare three different experimental termination rules in four treatments: a known finite end, an unknown end, and two variants with a random termination rule (with a high and with a low continuation probability, where cooperation can occur in a subgame-perfect equilibrium only with the high probability). We find that the termination rules do not significantly affect average cooperation rates. Specifically, employing a random termination rule does not cause significantly more cooperation compared to a known finite horizon, and the continuation probability does not significantly affect average cooperation rates either. However, the termination rules may influence cooperation over time and end-game behavior. Further, the (expected) length of the game significantly increases cooperation rates. The results suggest that subjects may need at least some learning opportunities (like repetitions of the supergame) before significant backward induction arguments in finitely repeated game have force. -- |
| Keywords: | Prisoner's dilemma,Repeated games,Infinite-horizon games,Experimental economics |
| JEL: | C72 C92 D21 D43 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:dicedp:19&r=gth |
| By: | Yosef Rinott; Marco Scarsini; Yaming Yu |
| Abstract: | Based on a model introduced by Kaminsky, Luks, and Nelson (1984), we consider a zero-sum allocation game called the Gladiator Game, where two teams of gladiators engage in a sequence of one-to-one fights in which the probability of winning is a function of the gladiators' strengths. Each team's strategy consist the allocation of its total strength among its gladiators. We find the Nash equilibria of the game and compute its value. To do this, we study interesting majorization-type probability inequalities concerning linear combinations of Gamma random variables. |
| Keywords: | Allocation game, Colonel Blotto game, David and Goliath, exponential distribution, Nash equilibrium, probability inequalities, unimodal distribution. |
| Date: | 2011–04–08 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp571&r=gth |
| By: | McMahon, Michael (University of Warwick) |
| Abstract: | Using an experiment, I compare the use of the `Beer Distribution' classroom game with the more traditional `chalk and talk' approach to teach students about inventories and the macroeconomy. My empirical results confirm and extend our understanding of the relative strengths and weaknesses of the use of classroom games : the game tends to improve interest and motivation on average, though some students dislike their use ; the game is e ective at driving home its key messages, but it may wrongly lead students to disregard other important factors ; the game is inferior where facts mastery or definitional learning is required. Rather than an endorsement or a criticism of classroom games, the conclusion is cautionary advice on how to best make use of games within an overall course. Key words: Classroom experiments and games ; motivation ; student learning outcomes JEL classification: A22 ; C90 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:964&r=gth |
| By: | John Kennes (School of Economics and Management, Aarhus University, Denmark); Daniel Monte (Department of Economics, Simon Fraser University, Canada); Norovsambuu Tumennasan (School of Economics and Management, Aarhus University, Denmark) |
| Abstract: | In this paper we take the mechanism design approach to the problem of assigning children of different ages to daycares, motivated by the mechanism currently in place in Denmark. This problem is similar to the school choice problem, but has two distinguishing features. First, it is characterized by an overlapping generations structure. For example, children of different ages may be allocated to the same daycare, and the same child may be allocated to different daycares across time. Second, the daycares' priorities are history-dependent: a daycare gives priority to children currently enrolled in it, as is the case with the Danish system. We first study the concept of stability, and, to account for the dynamic nature of the problem, we propose a novel solution concept, which we call strong stability. With a suitable restriction on the priority orderings of schools, we show that strong stability and the weaker concept of static stability will coincide. We then extend the well known Gale-Shapley deferred acceptance algorithm for dynamic problems and show that it yields a matching that satisfies strong stability. It is not Pareto dominated by any other matching, and, if there is an efficient stable matching, it must be the Gale-Shapley one. However, contrary to static problems, it does not necessarily Pareto dominate all other strongly stable mechanisms. Most importantly, we show that the Gale-Shapley algorithm is not strategy-proof. In fact, one of our main results is a much stronger impossibility result: For the class of dynamic matching problems that we study, there are no algorithms that satisfy strategy-proofness and strong stability. Second, we show that the also well known Top Trading Cycles algorithm is neither Pareto efficient nor strategy-proof. We conclude by proposing a variation of the serial dictatorship, which is strategyproof and efficient. |
| Keywords: | daycare assignment, market design, matching, overlapping generations, weak and strong stability, efficiency |
| JEL: | C78 D61 D78 I20 |
| Date: | 2011–05–23 |
| URL: | http://d.repec.org/n?u=RePEc:aah:aarhec:2011-05&r=gth |
| By: | Mikhail Golosov (Dept. of Economics, Yale University); Vasiliki Skreta (NYU, Stern School of Business); Aleh Tsyvinski (Dept. of Economics, Yale University); Andrea Wilson (NYU) |
| Abstract: | This paper studies strategic information transmission in a dynamic environment where, each period, a privately informed expert sends a message and a decision maker takes an action. Our main result is that, in contrast to a static environment, full information revelation is possible. The gradual revelation of information and the eventual full revelation is supported by the dynamic rewards and punishments. The construction of a fully revealing equilibrium relies on two key features. The first feature is that the expert is incentivized, via appropriate actions, to join separable groups in which she initially pools with far-away types, then later reveals her type. The second feature is the use of trigger strategies. The decision maker is incentivized by the reward of further information revelation if he chooses the separation-inducing actions, and the threat of a stop in information release if he does not. Our equilibrium is non-monotonic. With monotonic partition equilibria, full revelation is impossible. |
| Keywords: | Asymmetric information, Cheap talk, Dynamic strategic communication, Full information revelation |
| JEL: | D82 D83 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1802&r=gth |
| By: | Daron Acemoglu; Matthew O. Jackson |
| Abstract: | We study the evolution of the social norm of "cooperation" in a dynamic environment. Each agent lives for two periods and interacts with agents from the previous and next generations via a coordination game. "History" matters because agents only receive noisy information about the play of the previous generation and their interpretation of these signals is shaped by history. We characterize the conditions under which history completely drives equilibrium play, leading to a social norm of high or low cooperation. The impact of history is potentially countered by "prominent" agents, whose actions are more visible (in our baseline model, observed by all future agents), and who can leverage their greater visibility to influence expectations of other agents and overturn social norms of low cooperation. We also show that in equilibria not completely driven by history, there is a pattern of "reversion" whereby play starting with high (low) cooperation reverts toward lower (higher) cooperation. We study the evolution of the social norm of "cooperation" in a dynamic environment. Each agent lives for two periods and interacts with agents from the previous and next generations via a coordination game. "History" matters because agents only receive noisy information about the play of the previous generation and their interpretation of these signals is shaped by history. We characterize the conditions under which history completely drives equilibrium play, leading to a social norm of high or low cooperation. The impact of history is potentially countered by "prominent" agents, whose actions are more visible (in our baseline model, observed by all future agents), and who can leverage their greater visibility to influence expectations of other agents and overturn social norms of low cooperation. We also show that in equilibria not completely driven by history, there is a pattern of "reversion" whereby play starting with high (low) cooperation reverts toward lower (higher) cooperation. |
| JEL: | C72 C73 D7 P16 Z1 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:17066&r=gth |
| By: | Balogh, Tamás L.; Tasnádi, Attila |
| Abstract: | We determine the endogenous order of moves in a mixed price-setting duopoly. In contrast to the existing literature on mixed oligopolies we establish the payoff equivalence of the games with an exogenously given order of moves. Hence, it does not matter whether one becomes a leader or a follower. We also establish that replacing a private firm by a public firm in the standard Bertrand-Edgeworth game with capacity constraints increases social welfare and that a pure-strategy equilibrium always exists. |
| Keywords: | Bertrand-Edgeworth; mixed duopoly; timing games |
| JEL: | L13 D43 |
| Date: | 2011–05–19 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30993&r=gth |
| By: | Wolfgang Buchholz; Richard Cornes; Dirk Rübbelke |
| Abstract: | Matching mechanisms are regarded as an important instrument to bring about Pareto optimal allocations in a public good economy and to cure the underprovision problem associated with private provision of public goods. The desired Pareto optimal interior match-ing equilibrium, however, emerges only under very special conditions. But we show in this note that corner solutions, in which some agents choose zero flat contributions, normally avoid underprovision and illustrate and interpret our results by a simple numerical example. |
| JEL: | C78 H41 |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:acb:cbeeco:2011-541&r=gth |
| By: | Puppe, Clemens; Tasnádi, Attila |
| Abstract: | In a framework with two parties, deterministic voter preferences and a type of geographical constraints, we propose a set of simple axioms and show that they jointly characterize the districting rule that maximizes the number of districts one party can win, given the distribution of individual votes (the 'optimal gerrymandering rule'). As a corollary, we obtain that no districting rule can satisfy our axioms and treat parties symmetrically. -- |
| Keywords: | districting,gerrymandering |
| JEL: | D72 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:kitwps:24&r=gth |
| By: | Richard Cornes; Jun-ichi Itaya; Aiko Tanaka |
| Abstract: | We consider a two-stage voluntary provision model where individuals in a family contribute to a pure public good and/or a household public good, and, at the same time, the parent makes private transfers to her child within the same family. We show not only that Warr’s neutrality holds regardless of the different timings of parent-to-child transfers, but also that there is a continuum of Nash equilibria in the sense that individuals’ contributions and parental transfers are indeterminate, although the allocation of each’s private consumption and total public good provision is uniquely determined. We further show that, even in the presence of impure altruism or productivity difference in supplying public goods, neutrality and uniqueness of the equilibrium allocation may persist. |
| JEL: | C72 D64 H41 |
| Date: | 2011–04 |
| URL: | http://d.repec.org/n?u=RePEc:acb:cbeeco:2011-542&r=gth |
| By: | Bhattacharyya, Ranajoy; Saha, Bibhas |
| Abstract: | In a standard model of vertical differentiation, wage is assumed to determine the quality. Wage is also subject to bargaining. Increased bargaining power of the worker in the low quality firm reduces quality differential, and increases price competitiveness. The Opposite happens from a similar change in the high quality firm. |
| Keywords: | Wage bargaining; Quality competition |
| JEL: | C7 |
| Date: | 2011–05–20 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30968&r=gth |