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on Game Theory |
| By: | Jung, Hanjoon Michael |
| Abstract: | A pillage game is a coalitional game that is meant to be a model of Hobbesian anarchy. The spatial pillage game introduces a spatial feature into the pillage game by assuming that players are located in regions. Players can travel from one region to another in one move and can form a coalition and combine their power only with players in the same region. A coalition has power only within its region. Under this spatial restriction, some members of a coalition can pillage less powerful coalitions without any cost. The feasibility of pillages between coalitions determines the dominance relation. Core, stable set, and farsighted core are adopted as alternative solution concepts. |
| Keywords: | allocation by force; coalitional games; pillage game; spatial restriction; stable set; farsighted core |
| JEL: | C71 R19 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:4651&r=gth |
| By: | Voorneveld, Mark (Dept. of Economics, Stockholm School of Economics) |
| Abstract: | In classical game theory, players have finitely many actions and evaluate outcomes of mixed strategies using a von Neumann-Morgenstern utility function. Allowing a larger, but countable, player set introduces a host of phenomena that are impossible in finite games. <p> Firstly, in coordination games, all players have the same preferences: switching to a weakly dominant action makes everyone at least as well off as before. Nevertheless, there are coordination games where the best outcome occurs if everyone chooses a weakly dominated action, while the worst outcome occurs if everyone chooses the weakly dominant action. <p> Secondly, the location of payoff-dominant equilibria behaves capriciously: two coordination games that look so much alike that even the consequences of unilateral deviations are the same may nevertheless have disjoint sets of payoff-dominant equilibria. <p> Thirdly, a large class of games has no (pure or mixed) Nash equilibria. Following the proverb ``the grass is always greener on the other side of the hedge'', greener-grass games model constant discontent: in one part of the strategy space, players would rather switch to its complement. Once there, they'd rather switch back. |
| Keywords: | coordination games; dominant strategies; payoff-dominance; nonexistence of equilibrium; tail events |
| JEL: | C72 |
| Date: | 2007–08–28 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:hastef:0673&r=gth |
| By: | Carraro, Carlo; Sgobbi, Alessandra |
| Abstract: | The relevance of bargaining to everyday life can easily be ascertained, yet the study of any bargaining process is extremely hard, involving a multiplicity of questions and complex issues. The objective of this paper is to provide new insights on some dimensions of the bargaining process – asymmetries and uncertainties in particular – by using a non-cooperative game theory approach. We develop a computational model which simulates the process of negotiation among more than two players, who bargain over the sharing of more than one pie. Through numerically simulating several multiple issues negotiation games among multiple players, we identify the main features of players’ optimal strategies and equilibrium agreements. As in most economic situations, uncertainty crucially affects also bargaining processes. Therefore, in our analysis, we introduce uncertainty over the size of the pies to be shared and assess the impacts on players’ strategic behaviour. Our results confirm that uncertainty crucially affects players’ behaviour and modify the likelihood of a self-enforcing agreement to emerge. The model proposed here can have several applications, in particular in the field of natural resource management, where conflicts over how to share a resource of a finite size are increasing. |
| Keywords: | bargaining; non-cooperative game theory; simulation models; uncertainty |
| JEL: | C61 C71 C78 |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:6424&r=gth |
| By: | Eduardo Faingold (Cowles Foundation, Yale University); Yuliy Sannikov (Dept. of Economics, UC Berkeley) |
| Abstract: | We study a class of continuous-time reputation games between a large player and a population of small players in which the actions of the large player are imperfectly observable. The large player is either a normal type, who behaves strategically, or a behavioral type, who is committed to playing a certain strategy. We provide a complete characterization of the set of sequential equilibrium payoffs of the large player using an ordinary differential equation. In addition, we identify a sufficient condition for the sequential equilibrium to be unique and Markovian in the small players' posterior belief. An implication of our characterization is that when the small players are certain that they are facing the normal type, intertemporal incentives are trivial: the set of equilibrium payoffs of the large player coincides with the convex hull of the set of static Nash equilibrium payoffs. |
| Keywords: | Repeated games, Reputation, Continuous time |
| JEL: | C73 |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1624&r=gth |
| By: | Ed Hopkins; Tatiana Kornienko |
| Date: | 2007–08–31 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levrem:122247000000001442&r=gth |
| By: | Jung, Hanjoon Michael |
| Abstract: | This paper studies the possibility of cooperation based on players' preferences. Consider the following infinitely repeated game, similar to Ghosh and Ray (1996). At each stage, uncountable numbers of players are randomly matched without information about their partners' past actions and play a prisoner's dilemma game. The players have the option to continue their relationship, and they all have the same discount factor. Also, they have two possible types: high ability player (H) or low ability player (L). H can produce better outcomes for its partner as well as for itself than L can. I look for an equilibrium that is robust against both pair-wise deviation and individual deviation and call such equilibrium a social equilibrium. I show that in this setting, long term cooperative behavior can arise in a social equilibrium. H wants to match and play only with another H because an HH match produces better outcomes for H than an HL match. So H would break a match with L to increase the possibility of meeting another H, and thus H would not play any cooperative action with L. L knows this intention of H and realizes that L can only cooperate with another L. Consequently, both HH and LL matches are endowed with a scarcity value. This scarcity value is utilized by players to sustain cooperative relationships. Therefore, in a social equilibrium, whole players can play long term cooperative actions because of their preferences for their partners' types. |
| Keywords: | Folk theorem; Random-matching; Social equilibrium; Type-based payoffs |
| JEL: | C71 C78 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:4650&r=gth |
| By: | Michele Lombardi (Queen Mary, University of London); Marco Mariotti (Queen Mary, University of London) |
| Abstract: | An <i>uncovered bargaining solution</i> is a bargaining solution for which there exists a complete and strict relation (tournament) such that, for each feasible set, the bargaining solution set coincides with the uncovered set of the tournament. We provide a characterization of a class of uncovered bargaining solutions. |
| Keywords: | Bargaining, Tournaments, Uncovered set, Non-convex problems |
| JEL: | C72 D44 |
| Date: | 2007–09 |
| URL: | http://d.repec.org/n?u=RePEc:qmw:qmwecw:wp608&r=gth |
| By: | Roy, Sunanda; Sabarwal, Tarun |
| Abstract: | This paper studies comparative statics of equilibria in models where the optimal responses under consideration are (weakly) decreasing in endogenous variables, and (weakly) increasing in exogenous parameters. Such models include parameterized games of strategic substitutes. The analysis provides a sufficient condition for existence of increasing equilibria at a higher parameter value. This condition is presented first for best-response functions; it can be translated easily to payoff functions with one-dimensional individual strategy spaces, and it has a natural analogue to best-response correspondences. The condition is tight in the sense that with a weakenened condition, the same result may not obtain. The results here apply to asymmetric equilibria, and are applied to two classes of examples -- Cournot duopoly and tournaments. Moreover, sufficient conditions are presented to exhibit strong comparative statics of equilibria (that is, every equilibrium at a higher parameter value is greater than a given equilibrium at a lower parameter value), and to show existence of increasing equilibrium selections. |
| Keywords: | Monotone comparative statics; Weakly decreasing functions; Strategic substitutes; Payoff functions |
| JEL: | C60 C72 |
| Date: | 2005–05 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:4709&r=gth |
| By: | Larrosa, Juan MC |
| Abstract: | Two countries face a strategic interdependence in producing intermediate goods. Producing these intermediate goods requires both of domestic capital and another imported intermediate good. Individually they determine its balanced growth path by taking into account this interdependence. By allowing for strategic interactions in the analysis we adapted a two-agent dynamic setting and find an interior Markov Perfect Equilibrium (MPE) as well as an open-loop equilibrium. We find that main results resemble each other but growth rates will be higher when strategies are allowed to be revised dynamically. |
| Keywords: | Difference games; Economic growth; Intermediate goods. |
| JEL: | C73 F15 |
| Date: | 2007–08–30 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:4675&r=gth |
| By: | Juergen Huber (University of Innsbruck); Martin Shubik (Cowles Foundation, Yale University); Shyam Sunder (Yale University) |
| Abstract: | In this experiment we examine the performance of three minimal strategic market games relative to theoretical predictions. These models of a closed exchange economy with monetary and financial structures have limited amounts of cash to facilitate transactions. Subsequent experiments will deal with credit limitations, banking and credit, the role of clearinghouses and the possibility for the universal issue of credit by individuals. In theory, with enough money the non-cooperative equilibria should converge to the respective competitive equilibria as the number of players increases. Since general equilibrium theory abstracts away from the market mechanism, it makes no predictions about how the paths of convergence to the CE may differ across market mechanisms. GE allows no role for money or credit. In contrast to most market experiments conducted in open or partial equilibrium settings, we report on closed settings that include feedbacks. Laboratory examination of the three market mechanisms reveals convergence to CE with increasing number of players. It also reveals significant differences in the convergence paths across the mechanisms, suggesting that to the extent deviations from CE are of interest (either because the number of players in the environment of substantive interest is small, or because disequilibrium behavior itself is of substantive interest), theoretical abstraction from the market mechanisms has been taken too far. For example, the oligopoly effect of feedback from buying a good that the player is endowed with is missed. Inclusion of mechanism differences into theory would help us understand markets better. |
| Keywords: | Strategic market games, Laboratory experiments, General equilibrium |
| JEL: | C92 D43 D51 D58 L13 |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1623&r=gth |
| By: | Jörg Franke |
| Abstract: | In this paper a contest game with heterogeneous players is analyzed in which heterogeneity could be the consequence of past discrimination. Based on the normative perception of the heterogeneity there are two policy options to tackle this heterogeneity: either it is ignored and the contestants are treated equally, or affirmative action is implemented which compensates discriminated players. The consequences of these two policy options are analyzed for a simple two-person contest game and it is shown that the frequently criticized trade-off between affirmative action and total effort does not exist: Instead, affirmative action fosters effort incentives. A generalization to the n-person case and to a case with a partially informed contest designer yields the same result if the participation level is similar under each policy. |
| Keywords: | Asymmetric contest; affirmative action; discrimination |
| JEL: | C72 D63 I38 J78 |
| Date: | 2007–07–31 |
| URL: | http://d.repec.org/n?u=RePEc:aub:autbar:711.07&r=gth |
| By: | Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group); M. Vittoria Levati (Max Planck Institute of Economics, Strategic Interaction Group); Torsten Weiland (Max Planck Institute of Economics, Strategic Interaction Group) |
| Abstract: | In a public goods experiment, subjects can vary over a period of stochastic length two contribution levels: one is publicly observable (their cheap talk stated intention), while the other is not seen by the others (their secret intention). When the period suddenly stops, participants are restricted to choose as actual contribution either current alternative. Based on the two types of choice data for a partners and a perfect strangers condition, we confirm that final outcomes strongly depend on the matching protocol. As to choice dynamics, we distinguish different types of adaptations. |
| Keywords: | Public goods game, Cheap talk communication, Real-time protocol |
| JEL: | C72 H41 D82 D83 |
| Date: | 2007–08–20 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2007-048&r=gth |