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on Game Theory |
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Issue of 2013‒07‒05
twelve papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Naoki Funai |
| Abstract: | In this paper, we provide a theoretical prediction of the way in which adaptive players behave in the long run in games with strict Nash equilibria. In the model, each player picks the action which has the highest assessment, which is a weighted average of past payoffs. Each player updates his assessment of the chosen action in an adaptive manner. Almost sure convergence to a Nash equilibrium is shown under one of the following conditions: (i) that, at any non-Nash equilbrium action profile, there exists a player who can find another action which gives always better payoffs than his current payoff, (ii) that all non-Nash equilibrium action profiles give the same payoff. We show almost sure convergence to a Nash equilibrium in the following games: pure coordination games; the battle of the sexes games; the stag hunt game; and the first order static game. In the game of chicken and market entry games, players may end up playing a maximum action profile. |
| Keywords: | Adaptive Learning, Coordination Games |
| JEL: | C72 D83 |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:bir:birmec:13-14&r=gth |
| By: | Grant, Simon; Meneghel, Idione; Tourky, Rabee |
| Abstract: | Abstract. We define and discuss Savage games, which are ordinal games that are set in L. J. Savage’s framework of purely subjective uncertainty. Every Bayesian game is ordinally equivalent to a Savage game. However, Savage games are free of priors, prob- abilities and payoffs. Players’ information and subjective attitudes toward uncertainty are encoded in the state-dependent preferences over state contingent action profiles. In the games we study player preferences satisfy versions of Savage’s sure thing principle and small event continuity postulate. An axiomatic innovation is a strategic analog of Savage’s null events. We prove the existence of equilibrium in Savage games. This result eschews any notion of objective randomization, convexity, and monotonicity. Applying it to games with payoffs we show that our assumptions are satisfied by a wide range of decision-theoretic models. In this regard, Savage games afford a tractable framework to study attitudes towards uncertainty in a strategic setting. We illustrate our results on the existence of equilibrium by means of examples of games in which players have expected and non-expected utility. |
| Keywords: | Bayesian games, multiple priors, non-expected utility, subjective uncer- tainty, existence of equilibrium, decomposable sets., Risk and Uncertainty, D81, C7, |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:ags:uqsers:151501&r=gth |
| By: | Yakov Babichenko |
| Abstract: | We study the query complexity of approximate notions of Nash equilibrium in games with large number of players n and constant number of actions m. Our main result states that even for constant {\epsilon}, the query complexity of {\epsilon}-well supported Nash equilibrium is exponential in n. |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1306.6686&r=gth |
| By: | Pedro Dal Bó; Enrique R. Pujals |
| Abstract: | We study the evolutionary robustness of strategies in innitely repeated prisoners' dilemma games in which players make mistakes with a small probability and are patient. The evolutionary process we consider is given by the replicator dynamics. We show that there are strategies with a uniformly large basin of attraction independent of the size of the population. Moreover, we show that those strategies forgive defections and, assuming that they are symmetric, they cooperate. We provide partial eciency results for asymmetric strategies. |
| Keywords: | # |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2013-5&r=gth |
| By: | Tonin, Simone (Department of Economics, University of Warwick,) |
| Abstract: | This short paper shows in an example of strategic market game that the Cournot-Nash equilibrium converges to the Walras equilibrium, even in the case of an exchange economy with infinitely many commodities. |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:1005&r=gth |
| By: | Roland Pongou; Roberto Serrano |
| Abstract: | We study the long-run stability of trade 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-bene?t trade-o¤ results in each agent having a single-peaked utility over the number of partners?the volume of trade?, the peak being greater for men than for women. We propose a stochastic matching process in which self-interested agents form and sever links over time. Links can be added or deleted, sometimes simultaneously by a single agent. While the unperturbed process yields each pairwise stable network as an absorbing state, stochastic stability in two perturbed processes provides a signi?cant re?nement, leading respectively to egalitarian and anti-egalitarian pairwise stable networks. This has implications for the concentration on each side of the market of a random information shock. The analysis captures stylized facts, related to market fragmentation, concentration and contagion asymmetry, in several two-sided economies. |
| Keywords: | Two-sided networks, pairwise stability, stochastic stability, herd externality, informational cascade, fragmentation, concentration, economy thinness, contagion asymmetry. |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2013-6&r=gth |
| By: | Eric Bahel (Department of Economics, Virginia Polytechnic Institute and State University); Christian Trudeau (Department of Economics, University of Windsor) |
| Abstract: | In the discrete cost sharing model with technological cooperation (Bahel and Trudeau (IJGT, 2013)), we study the implications of a number of properties that strengthen the well-known Dummy axiom. Our main axiom, which requires that costless units of demands do not affect the cost shares, is used to characterize two classes of rules. Combined with anonymity and a specific stability property, this requirement picks up sharing methods that allow the full compensation of at most one technological contribution. If instead we strengthen the well-known Dummy property to include agents whose technological contribution is offset by the cost of their demand, we are left with an adaptation of the Shapley-Shubik method that treats technologies as private and rewards their contributions. Our results provide two interesting axiomatizations for the adaptations of the Shapley-Shubik rule to our framework. |
| Keywords: | Shapley-Shubik, Technological Cooperation, Dummy |
| JEL: | C71 D63 |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:wis:wpaper:1304&r=gth |
| By: | Massimiliano Castellani (Department of Economics, University of Bologna, Italy; The Rimini Centre for Economic Analysis, Italy); Luca Fanelli (Department of Statistical Sciences, University of Bologna, Italy); Marco Savioli (Department of Economics, University of Siena, Italy; The Rimini Centre for Economic Analysis, Italy; School of Economics, Management, and Statistics, Rimini campus, University of Bologna, Italy) |
| Abstract: | In this paper, we propose a novel policy-game model with perfect information to analyze the simultaneous interaction between the government and the labour union in a unionized economy. Our model explains how the strategic interaction between the labour union, mainly concerned with wages and strikes, and the government, mainly concerned with unemployment and fiscal policy, gives rise to a long run Cournot-Nash equilibrium. Our policy-game model is estimated by a cointegrated Vector Autoregressive system using Italian quarterly data on government budget surplus (fiscal efforts) and on hours not worked (strikes) on the period 1960-2009. Since the government budget surplus is the variable which adjusts faster to equilibrium, our estimated speeds of long run adjustment point out that the government is more effective than the labour union. A phase diagram interpretation of the estimated model is provided. |
| Keywords: | Fiscal efforts, strikes, policy game, VEqC, speed of adjustment |
| JEL: | E62 J51 C72 C54 C32 |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:33_13&r=gth |
| By: | Halkos, George; Papageorgiou , George |
| Abstract: | This paper is concerned with the classic topic of intertemporal resource economics: the optimal harvesting of renewable natural resources over time by one and several resource owners with conflicting interests. The traditional management model, dating back to Plourde (1970), is extended towards a two–state model in which harvesting equipment is treated as a stock variable. As a consequence of this extension, equilibrium dynamics with bifurcations and limit cycles occur. We also discuss conflicts as a game with two types of players involved: the traditional fishermen armed with the basic equipment and the heavy equipment users. Both players have a common depletion function, considered as harvesting, which is dependent together on personal effort and on intensity of equipment’s usage. |
| Keywords: | Renewable resources; exploitation of natural resources; optimal control; differential games. |
| JEL: | C61 C62 Q30 Q32 |
| Date: | 2013–03 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:47871&r=gth |
| By: | Maria Gabriella Graziano (Università di Napoli Federico II and CSEF); Claudia Meo (Università di Napoli Federico II); Nicholas C. Yannelis (University of Iowa and University of Manchester) |
| Abstract: | An exchange economy with asymmetrically informed agents is considered with an exogenous rule that regulates the information sharing among agents. For it, the notion of stable sets à la Von Neumann and Morgenstern is analyzed. Two different frameworks are taken into account as regards preferences: a model without expectations and a model with expected utility. For the first one, it is shown that the set $V$ of all individually rational, Pareto optimal, symmetric allocations is the unique stable set of symmetric allocations. For the second one, an example is presented which shows that the same set $V$ is not externally stable and a weaker result is proved. Finally, the coalitional incentive compatibility of allocations belonging to the unique stable set is provided. |
| Keywords: | sets, asymmetric information, information sharing |
| JEL: | C71 D51 D82 |
| Date: | 2013–06–25 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:333&r=gth |
| By: | James Lake (Southern Methodist University) |
| Abstract: | In the presence of multilateral negotiations, are Free Trade Agreements (FTAs) necessary for, or will they prevent, free trade? This question is explored using a novel dynamic network theoretic model where countries are farsighted and asymmetric in terms of market size. I develop a new equilibrium concept that endogenizes the order of negotiations. FTAs are necessary for free trade when there are two small countries and one large country but FTAs prevent free trade when there are two large countries and one small country. The model provides insights into the dynamics of recent trade negotiations involving the US. |
| Keywords: | Free Trade Agreements, preference erosion, multilateralism, free trade, networks, farsighted |
| JEL: | C71 F12 F13 |
| Date: | 2013–06 |
| URL: | http://d.repec.org/n?u=RePEc:smu:ecowpa:1304&r=gth |
| By: | Brunner, Christoph; Hu, Audrey; Oechssler, Jörg |
| Abstract: | In premium auctions, the highest losing bidder receives a reward from the seller. This paper studies the private value English premium auction (EPA) for different risk attitudes of bidders. We explicitly derive the symmetric equilibrium for bidders with CARA utilities and conduct an experimental study to test the theoretical predictions. In our experiment, subjects are sorted into risk-averse and risk loving groups. We find that revenues in the EPA are significantly higher when bidders are risk loving rather than risk averse. These results are partly consistent with theory and confirm the general view that bidders’ risk preferences constitute an important factor that affects bidding behavior and consequently also the seller’s expected revenue. However, individual subjects rarely follow the equilibrium strategy and as a result, revenue in our experiment is lower than in the symmetric equilibrium. |
| Keywords: | premium auction; risk preference; Holt-Laury method; experimental economics. |
| Date: | 2013–06–03 |
| URL: | http://d.repec.org/n?u=RePEc:awi:wpaper:0544&r=gth |