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on Game Theory |
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Issue of 2011‒05‒24
twelve papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Bajoori Elnaz; Flesch János; Vermeulen Dries (METEOR) |
| Abstract: | We investigate the relations between different types of perfect equilibrium, introduced by Simon and Stinchcombe (1995) for games with compact action spaces and continuous payoffs. Simon and Stinchcombe distinguish two approaches to perfect equilibrium in this context, the classical "trembling hand'''' approach, and the so-called "finitistic'''' approach.We propose an improved definition of the finitistic approach, called global-limit-of-finite perfection, and prove its existence. Despite the fact that the finitistic approach appeals to basic intuition, our results---specifically examples (1) and (2)---seem to imply a severe critique on this approach. In the first example any version of finitistic perfect equilibrium admits a Nash equilibrium strategy profile that is not limit admissible. The second example gives a completely mixed (and hence trembling hand perfect) Nash equilibrium that is not finitistically perfect. Further examples illustrate the relations between the two approaches to perfect equilibrium and the relation to admissibility and undominatedness of strategies. |
| Keywords: | mathematical economics; |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2011029&r=gth |
| By: | Hirofumi Yamamura (Research Institute for Economics and Business Administration, Kobe University) |
| Abstract: | We study a one-dimensional voting game in which voters choose a policy from a one-dimensional policy set over which voters have single-peaked preferences. The purpose of this paper is to analyze coalitional behaviors under any given voting mechanism. We employ the notion of strong Nash equilibrium and identify a necessary and su¢ cient condition for a voting mechanism to possess a strong Nash equilibrium by using the minimax theorem. We moreover show that any strong Nash outcome, if it exists, results in an outcome recommended by a particular augmented median voter rule. |
| Keywords: | Single-peakedness, Augmented median voter rule, Strong Nash equilibrium, Coalition-proof Nash Equilibrium, Minimax theorem, Manipulation. |
| JEL: | D78 D72 C70 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:kob:dpaper:dp2011-21&r=gth |
| By: | Lombardi, Michele; Yoshihara, Naoki |
| Abstract: | Noting that a full characterization of Nash-implementation is given using a canonical-mechanism and Maskin’s theorem (Maskin, 1999) is shown using a mechanism with Saijo’s type of strategy space reduction (Saijo, 1988), this paper fully characterizes the class of Nashimplementable social choice correspondences (SCCs) by mechanisms endowed with Saijo’s message space specification - s-mechanisms. This class of SCCs is further shown to be equivalent to the class of Nashimplementable SCCs, though any further ‘strategy space reduction’ mechanism breaks this equivalent relationship down. |
| Keywords: | Nash implementation, strategy space reduction, s-mechanisms, Condition μsr, Condition Ms |
| JEL: | C72 D71 D82 |
| Date: | 2011–04 |
| URL: | http://d.repec.org/n?u=RePEc:hit:hituec:a548&r=gth |
| By: | Duffy, Sean; Smith, John |
| Abstract: | We find that differences in the ability to devote cognitive resources to a strategic interaction imply differences in strategic behavior. In our experiment, we manipulate the availability of cognitive resources by applying a differential cognitive load. In cognitive load experiments, subjects are directed to perform a task which occupies cognitive resources, in addition to making a choice in another domain. The greater the cognitive resources required for the task implies that fewer such resources will be available for deliberation on the choice. Although much is known about how subjects make decisions under a cognitive load, little is known about how this affects behavior in strategic games. We run an experiment in which subjects play a repeated multi-player prisoner's dilemma game under two cognitive load treatments. In one treatment, subjects are placed under a high cognitive load (given a 7 digit number to recall) and subjects in the other are placed under a low cognitive load (given a 2 digit number). We find that the individual behavior of the subjects in the low load condition converges to the Subgame Perfect Nash Equilibrium prediction at a faster rate than those in the high load treatment. However, we do not find the corresponding relationship involving outcomes in the game. Specifically, there is no evidence of a significantly different convergence of game outcomes across treatments. As an explanation of these two results, we find evidence that low load subjects are better able to adjust their choice in response to outcomes in previous periods. |
| Keywords: | cognitive resources; experimental economics; experimental game theory; public goods game |
| JEL: | C72 C91 |
| Date: | 2011–05–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:30856&r=gth |
| By: | Cheung, Stephen L. (University of Sydney) |
| Abstract: | This paper introduces new experimental designs to enrich understanding of conditional cooperation and punishment in public good games. The key to these methods is to elicit complete contribution or punishment profiles using the strategy method. It is found that the selfish bias in conditional cooperation is made significantly worse when other players contribute more unequally. Contingent punishment strategies are found to increase with decreasing contributions by the target player and also increasing contributions by a third player. "Antisocial" punishments are not directed specifically toward high contributors, but may be motivated by pre-emptive retaliation against punishment a player expects to incur. |
| Keywords: | conditional cooperation, selfish bias, punishment, public good experiment, strategy method |
| JEL: | C72 C91 D70 H41 |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp5689&r=gth |
| By: | Swee-Hoon Chuah (Nottingham University Business School); Robert Hoffmann (Nottingham University Business School); Jeremy Larner (Nottingham University Business School) |
| Abstract: | The standard chicken game is a popular model of certain important real scenarios but does not allow for the escalation behaviour these are typically associated with. This is problematic if the critical, final decisions in these scenarios are sensitive to previous escalation. We introduce and analyse, theoretically and by experiment, a new game which permits escalation behaviour. Compared with an equivalent chicken game, Pareto-suboptimal outcomes are significantly more frequent. This result is inconsistent with our rational choice analysis and possible psychological roots are explored. |
| Keywords: | Escalation, Brinkmanship, Chicken game, Experiments |
| JEL: | C72 C78 C91 |
| Date: | 2011–05–13 |
| URL: | http://d.repec.org/n?u=RePEc:bbr:workpa:16&r=gth |
| By: | Richard Barrett; Ioanna Kokores; Somnath Sen |
| Abstract: | Central banks, in executing monetary policy, while pursuing traditional objectives, such as the control of inflation, may try also to promote financial stability. In this paper, we explore a simple monetary policy game played between the central bank and the financial sector. The central bank can be of two types, one traditional and the other concerned with controlling the financial markets; however, the financial sector is unsure which, due to incomplete information. The conclusion of the paper is that for small shocks to inflation there is a pooling equilibrium, whereas for larger shocks there is separation. In the latter case, central bank concern for the stability of the financial sector is outed. We conclude by relating our results to the recent worldwide financial crisis. |
| Keywords: | Monetary policy, central bank, financial stability, strategic behaviour, incomplete information |
| JEL: | E44 E52 E58 E61 |
| Date: | 2011–04 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:11-10&r=gth |
| By: | Christoph Engel (Max Planck Institute for Research on Collective Goods, Bonn); Sebastian Kube (Max Planck Institute for Research on Collective Goods, Bonn); Michael Kurschilgen (Max Planck Institute for Research on Collective Goods, Bonn) |
| Abstract: | Cooperation problems are at the heart of many everyday situations. In this paper, we propose a very simple and light-handed mechanism to sustain cooperation and test its performance in a rich laboratory environment. The mechanism moderates cooperation by controlling experiences, more specifically, it "manipulates" subjects’ initial beliefs by providing them with selective information about (un)cooperative behavior in other, unrelated, groups. We observe that contributions are considerably sensitive to such selective information. First impressions participants happen to make predict subsequent behavior. Our results, however, suggest an asymmetry in the strength of the reaction – which might pose a limit on the effectiveness of the mechanism in natural settings. |
| Date: | 2011–03 |
| URL: | http://d.repec.org/n?u=RePEc:mpg:wpaper:2011_05&r=gth |
| By: | Sophie Bade (Max Planck Institute for Research on Collective Goods, Bonn) |
| Abstract: | This article is concerned with the welfare properties of trade when the behavior of agents cannot be rationalized by preferences. I investigate this question in an environment of matching allocation problems. There are two reasons for doing so: rstly, the niteness of such problems entails that the domain of the agents' choice behavior does not need to be restricted in any which way to obtain results on the welfare properties of trade. Secondly, some matching allocation mechanisms have been designed for non-market environments in which we would typically expect boundedly rational behavior. I nd qualied support for the statements that all outcomes of trade are Pareto-optimal and all Pareto optima are reachable through trade. Contrary to the standard case, dierent trading mechanisms lead to dierent outcome sets when the agents' behavior is not rationalizable. These results remain valid when restricting attention to \minimally irrational" behavior. |
| Keywords: | Bounded Rationality, House Allocation Problems, Fundamental Theorems of Welfare, Multiple Rationales |
| JEL: | C78 D60 |
| Date: | 2010–12 |
| URL: | http://d.repec.org/n?u=RePEc:mpg:wpaper:2010_47&r=gth |
| By: | Ignacio Monzon; Michael Rapp |
| Abstract: | Observational learning is typically examined when agents have precise information about their position in the sequence of play. We present a model in which agents are uncertain about their positions. Agents are allowed to have arbitrary ex-ante beliefs about their positions: they may observe their position perfectly, imperfectly, or not at all. Agents sample the decisions of past individuals and receive a private signal about the state of the world. We show that social learning is robust to position uncertainty. Under any sampling rule satisfying a stationarity assumption, learning is complete if signal strength is unbounded. In cases with bounded signal strength, we show that agents achieve what we define as constrained efficient learning: individuals do at least as well as the most informed agent would do in isolation. |
| Keywords: | social learning; information aggregation; herds; position uncertainty; observational learning |
| JEL: | C72 D83 D85 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:cca:wpaper:206&r=gth |
| By: | Bejerano, Hernan; Latek, Maciej M. |
| Keywords: | Marketing, |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:ags:aaea11:103900&r=gth |
| By: | D. Pinheiro; A. A. Pinto; S. Z. Xanthopoulos; A. N. Yannacopoulos |
| Abstract: | We study a bargaining scheme under which two agents update their beliefs about the future states of the world in order to reach an agreement on the price of a given contingent claim. We first formulate the problem as an optimization problem and prove the existence of a solution for such problem yielding a unique price for the contingent claim to be traded. We then proceed to study a discrete time projected gradient scheme whose orbits converge to the optimal point where the two agents agree on the price of contingent claim, thus modeling the evolution of the agents beliefs during the bargaining period. We conclude with an analysis of the special case where the two agents make their decisions under an exponential utility. |
| Date: | 2011–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1105.1767&r=gth |