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on Game Theory |
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Issue of 2013‒04‒13
sixteen papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Herings P.J.J.; Predtetchinski A. (GSBE) |
| Abstract: | At each moment in time, some alternative from a finite set is selected by a dynamic process. Players observe the alternative selected and sequentially cast a yes or a no vote. If the set of players casting a yes–vote is decisive for the alternative in question,the alternative is accepted and the game ends. Otherwise the next period begins.We refer to this class of problems as collective stopping problems. Collective choicegames, quitting games, and coalition formation games are particular examples that fit nicely into this more general framework.When the core of this game is non–empty, a stationary equilibrium in pure strategies is shown to exist. But in general, even mixed stationary equilibria may not exist in collective stopping games. We consider strategies that are pure and action–independent, and allow for a limited degree of history dependence. Under such individual behavior, aggregate behavior can be conveniently summarized by a collective strategy. We consider collective strategies that are simple and induced by two–step game–plans and provide a constructive proof that this collection always contains a subgame perfect equilibrium. The existence of such an equilibrium is shown to imply the existence of a sequential equilibrium in an extended model with incomplete information. Collective equilibria are shown to be robust to perturbations in the dynamic process and in utilities. We apply our approach to the case with three alternatives exhibiting a Condorcet cycle and to the Baron-Ferejohn model of redistributive politics. |
| Keywords: | Existence and Stability Conditions of Equilibrium; |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umagsb:2013014&r=gth |
| By: | Paula Jaramillo; Çagatay Kayi; Flip Klijn |
| Abstract: | This paper studies many-to-one matching markets where each student is assigned to a hospital. Each hospital has possibly multiple positions and responsive preferences. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling. Roth and Sotomayor (1990) showed that there can be unstable equilibrium outcomes. We prove that any stable matching can be obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the so-called "rural hospital theorem" cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to one-to-one matching markets, (a) filled positions depend on the particular equilibrium that is reached and (b) welfare levels are not bounded by the student and hospital-optimal stable matchings (with respect to the true preferences). |
| Keywords: | many-to-one matching, deferred acceptance, Nash equilibrium, dropping strategies, filled positions, welfare |
| JEL: | C78 D60 |
| Date: | 2013–04 |
| URL: | http://d.repec.org/n?u=RePEc:bge:wpaper:686&r=gth |
| By: | Pongou, Roland; Serrano, Roberto |
| Abstract: | We study the dynamic stability of networks in a two-sided economy of agents labelled men and women. Each agent desires relationships with the other type, but having multiple partners is costly. This cost-benefit trade-off results in each agent having a single-peaked utility function, the peak being greater for men than for women. We propose two stochastic Markov processes in which self-interested agents form and sever links over time, but may also take actions that do not increase their utility with small probability. In the first process, an agent who invests more time in a relationship signals commitment to his/her partner, whereas in the second, such an agent is perceived as having a weaker position. We prove that only egalitarian pairwise stable networks (in which all agents have the same number of partners) form in the long run under the first process, while under the second, only anti-egalitarian pairwise stable networks (in which all women are matched to a small number of men) arise. This latter outcome is also consistent with the presence of "herd externality" or "informational cascade", leading to a pattern of a one-sided thin market. Applying these results to communication shows that the diffusion of a given piece of information can widely vary across identical economies, and that information concentrates more in women than in men. The model sheds light on patterns of network formation in several two-sided markets, including employer-employee, dating, buyer-seller, and faculty-student relationships. |
| Keywords: | Two-sided networks, pairwise stability, stochastic stability, herd externality, informational cascade, contagion asymmetry, thin economy. |
| JEL: | A14 C7 I12 J00 |
| Date: | 2013–04–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:46021&r=gth |
| By: | Jona Linde (University of Amsterdam); Joep Sonnemans (University of Amsterdam); Jan Tuinstra (University of Amsterdam) |
| Abstract: | Minority games are a stylized description of strategic situations with both coordination and competition. These games are widely studied using either simulations or laboratory experiments. Simulations can show the dynamics of aggregate behavior, but the results of such simulations depend on the type of strategies used. So far experiments provided little guidance on the type of strategies people use because the set of possible strategies is very large. We therefore use a multi-round strategy method experiment to directly elicit people's strategies. Between rounds participants can adjust their strategy and test the performance of (possible) new strategies against strategies from the previous round. Strategies gathered in the experiment are subjected to an evolutionary competition. The strategies people use are very heterogeneous although aggregate outcomes resemble the symmetric Nash equilibrium. The strategies that survive evolutionary competition achieve much higher levels of coordination. |
| Keywords: | minority game; strategy experiment; evolution; simulation |
| JEL: | C63 C72 C91 D03 |
| Date: | 2013–03–07 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20130043&r=gth |
| By: | Einy, Ezra; Haimanko, Ori; Orzach, Ram; Sela, Aner |
| Abstract: | We study two-player common-value all-pay auctions (contests) with asymmetric information under the assumption that one of the players has an information advantage over his opponent. We characterize the unique equilibrium in these contests, and examine the role of information in determining the players' expected efforts, probabilities of winning, and expected payoffs. In particular, we show that the players always have the same probability of winning the contest, and that their expected efforts are the same, but their expected payoffs are different. It is also shown that budget constraints may have an unanticipated effect on the players' expected payoffs, i.e., a player's information advantage may turn into a payoff disadvantage. |
| Keywords: | all-pay auctions; asymmetric information; information advantage |
| JEL: | C72 D44 D82 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9315&r=gth |
| By: | Billand, Pascal; Bravard, Christophe; Kamphorst, Jurjen J.A.; Sarangi, Sudipta |
| Abstract: | Social networks, be it on the internet or in real life, facilitate information flows. We model this by giving agents incentives to link with others and receive information through those links. We consider networks where agents have an incentive to confirm the information they receive from others. Our paper analyzes the social networks that are formed. We first study the existence of Nash equilibria and then characterize the set of strict Nash networks. Next, we characterize the set of strictly efficient networks and discuss the relationship between strictly efficient networks and strict Nash networks. Finally, we check the robustness of our results by allowing for heterogeneity among agents, possibility of bilateral deviations of agents, and decay in the network. |
| Keywords: | connections model, confirmation, two-way flow models. |
| JEL: | C72 D85 |
| Date: | 2013–04 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:45835&r=gth |
| By: | Harold Houba (VU University Amsterdam); Gerard van der Laan (VU University Amsterdam); Yuyu Zeng (VU University Amsterdam) |
| Abstract: | We study multiple agents along a general river structure that is expressed by a geography matrix and who have access to limited local resources, quasi-linear preferences over water and money and cost functions dependent upon river inflow and own extraction. Unanimity bargaining determines the water allocation and monetary transfers. We translate International Water Law into either disagreement outcomes or individual aspiration levels. In the former case, we apply the asymmetric Nash bargaining solution, in the latter case the agents have to compromise in order to agree and we apply the asymmetric Nash rationing solution. In both cases the optimization problem is separable into two subproblems: the efficient water allocation that maximizes utilitarian welfare given the geography matrix; and the determination of the monetary transfers associated with the weights. We show that the Nash rationing solution may result in nonparticipation, therefore we generalize to the case with participation constraints. |
| Keywords: | River Basin Management; International Water Law; Negotiations; Externalities; Political Economy of Property Rights |
| JEL: | C70 D60 Q53 |
| Date: | 2013–04–02 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20130051&r=gth |
| By: | Matt Van Essen (Department of Economics, Finance, and Legal Studies, University of Alabama); John Wooders (Economics Discipline Group, University of Technology, Sydney) |
| Abstract: | We explore the role of experience in mixed-strategy games by comparing, for a stylized version of Texas Hold-em, the behavior of experts, who have extensive experience playing poker online, to the behavior of novices. We find significant differences. The initial frequencies with which players bet and call are closer to equilibrium for experts than novices. And, while the betting and calling frequencies of both types of subjects exhibit too much heterogeneity to be consistent with equilibrium play, the frequencies of experts exhibit less heterogeneity. We find evidence that the style of online play transfers from the field to the lab. |
| Keywords: | mixed-strategy Nash equilibrium; minimax; poker; experiment; expertise |
| JEL: | C72 C92 C93 D03 |
| Date: | 2013–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:uts:ecowps:6&r=gth |
| By: | Andrea Gallice (Department of Economics and Statistics (Dipartimento di Scienze Economico-Sociali e Matematico-Statistiche), University of Torino, Italy) |
| Abstract: | This paper introduces and discusses the concept of pu-dominance in the context of finite games in normal form. It then presents the pu-dominance criterion for equilibrium selection, a generalization of the risk-dominance criterion to games with more than two players. |
| Keywords: | equilibrium selection, normal form games, pu-dominance |
| JEL: | C72 C73 |
| Date: | 2013–03 |
| URL: | http://d.repec.org/n?u=RePEc:tur:wpapnw:019&r=gth |
| By: | Schmitz, Patrick W |
| Abstract: | In the property rights approach to the theory of the firm (Hart, 1995), parties bargain about whether or not to collaborate after non-contractible investments have been made. Most contributions apply the regular Nash bargaining solution. We explore the implications of using the generalized Nash bargaining solution. A prominent finding regarding the suboptimality of joint ownership turns out to be robust. However, in contrast to the standard property rights model, it may well be optimal to give ownership to a party whose investments are less productive, provided that this party's ex-post bargaining power is relatively small. |
| Keywords: | bargaining; incomplete contracts; investment incentives; ownership |
| JEL: | C78 D23 D86 L23 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9281&r=gth |
| By: | Konrad, Kai A.; Cusack, Thomas R. |
| Abstract: | What is the strategic role of membership in an intergovernmental group with unanimity requirements if the group negotiates with an external player in a setting with incomplete information? Being in such a group has a strategic effect compared to negotiating as a stand-alone player and reduces the demands of the outside player: being in a group lends additional bargaining power. Negotiating as a group may also cause more inefficiencies due to bargaining failure, and this might harm the intergovernmental group. We uncover the role of preference alignment and preference independence between members of the coalition group for equilibrium payoffs and welfare effects. In this analysis we also distinguish between coalition groups with and without side payments. Overall, coalition groups tend to perform well for the members of the coalition group in comparison to fully decentralized negotiations, particularly if the objectives of the members of the coalition group are not always perfectly aligned. -- |
| Keywords: | bargaining,incomplete information,coalitions,groups,strategic bargaining power |
| JEL: | F51 F53 F59 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbmbh:spii2013202&r=gth |
| By: | Bettina Klose (Department of Economics, University of Zurich); Dan Kovenock (Economic Science Institute, Chapman University) |
| Abstract: | We derive a necessary and sufficient condition for the existence of equilibria with only two active players in the all-pay auction with complete information and identity-dependent externalities. This condition shows that the generic equilibrium of the standard all-pay auction is robust to the introduction of "small" identity-dependent externalities. In general, however, the presence of identity-dependent externalities invalidates well-established qualitative results concerning the set of equilibria of the first-price all-pay auction with complete information. With identity-dependent externalities equilibria are generally not payoff equivalent, and identical players may earn different payoffs in equilibrium. These observations show that Siegel’s (2009) results characterizing the set of equilibrium payoffs in all-pay contests, including the all-pay auction as a special case, do not extend to environments with identity-dependent externalities. We further compare the all-pay auction with identity-dependent externalities to the first-price winner-pay auction with identity-dependent externalities. We demonstrate that the equilibrium payoffs of the all-pay auction and winner-pay auction cannot be ranked unambiguously in the presence of identity-dependent externalities by providing examples of environments where equilibrium payoffs in the all-pay auction dominate those in the winner-pay auction and vice versa. |
| Keywords: | All-pay auction, Identity-dependent externalities, Payoff nonequivalence, political conflict |
| JEL: | D44 D62 D72 C72 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:13-10&r=gth |
| By: | Araujo, Luis; Guimarães, Bernardo |
| Abstract: | This paper studies how constraints on the timing of actions affect equilibrium in intertemporal coordination problems. We show that while the possibility of waiting longer for others'’ actions helps agents to coordinate in the good equilibrium, the option of delaying one’s' actions harms coordination and can induce severe coordination failures: if agents are very patient, they might get arbitrarily low expected payoffs even in cases where coordination would yield arbitrarily large returns. The risk-dominant equilibrium of the corresponding one-shot game is selected when the option to delay effort is commensurate with the option to wait longer for others’' actions. In an application to innovation processes, we show that protection of the domestic industry might hinder industrialization. We also argue that increased competition might have spurred the emergence of shadow banking in the last few decades. |
| Keywords: | coordination failures; delay; option; strategic complementarities |
| JEL: | C72 C73 D84 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9294&r=gth |
| By: | Hans Gersbach (ETH Zurich); Hans Haller (Virginia Tech University); Hideo Konishi (Boston College) |
| Abstract: | We consider competitive markets for multiple commodities with endogenous formation of one- or two-person households. Within each two-person household, externalities from the partner's commodity consumption and unpriced actions are allowed. Each individual has two types of traits: observable characteristics and unobservable taste characteristics. Each individual gets utility from his/her own private consumption, from discrete actions such as job-choice, from the partner's observable characteristics such as appearance and hobbies, from some of the partner's consumption vectors, and from the partner's action choices. We investigate competitive market outcomes with an endogenous household structure in which no individual and no man/woman-pair can deviate profitably. We find a set of sufficient conditions under which a stable matching equilibrium exists. We further establish the first welfare theorem for this economy. |
| Keywords: | endogenous household formation of households, consumption externalities, stable matching equilibrium, efficiency |
| JEL: | D51 D61 D71 |
| Date: | 2013–03–31 |
| URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:821&r=gth |
| By: | Jinzhong Niu; Simon Parsons |
| Abstract: | In this paper, we introduce a novel, non-recursive, maximal matching algorithm for double auctions, which aims to maximize the amount of commodities to be traded. It differs from the usual equilibrium matching, which clears a market at the equilibrium price. We compare the two algorithms through experimental analyses, showing that the maximal matching algorithm is favored in scenarios where trading volume is a priority and that it may possibly improve allocative efficiency over equilibrium matching as well. A parameterized algorithm that incorporates both maximal matching and equilibrium matching as special cases is also presented to allow flexible control on how much to trade in a double auction. |
| Date: | 2013–02 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1304.3135&r=gth |
| By: | Jönsson, Stefan; Schmutzler, Armin |
| Abstract: | This paper analyzes how all-pay auctions with endogenous prizes can be used to provide effort incentives. We show that wide classes of effort distributions can be implemented as equilibrium outcomes of such games. We also ask how all-pay auctions have to be structured so as to induce high expected highest efforts without generating excessive wasteful efforts of losers. All-pay auctions with endogenous prizes can do better than all-pay auctions with fixed prizes in this respect, in particular, when the prize function is approximately linear. We use the results to compare patents and prizes as innovation incentives, and to explore promotion incentives in organizations. |
| Keywords: | all-pay auctions; contests; endogenous prizes; implementation |
| JEL: | D02 D43 D44 |
| Date: | 2013–01 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:9323&r=gth |