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on Game Theory |
| By: | Ehud Kalai |
| Abstract: | This short survey discusses recent findings on the robustness of Nash equilibria of strategic games with many semianonymous players. It describes the notion of structural robustness and its general consequences, as well as implications to particular games, such as ones played on the web and market games. |
| Keywords: | Nash Equilibrium,ex-post Nash, anonymous games, market games, rational expectations, structural robustness, information proofness, web games |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1431&r=gth |
| By: | Gulick,Gerwald van; Borm,Peter; De Waegenaere,Anja; Hendrickx,Ruud (Tilburg University, Center for Economic Research) |
| Abstract: | In a deposit game coalitions are formed by players combining their capital. The proceeds of their investments then have to be divided among those players. The current model extends earlier work on capital deposits by allowing reinvestment of returns. Two specific subclasses of deposit games are introduced. It is seen that each term dependent deposit game possesses a core element. Capital dependent deposit games are also shown to have a core element and even a population monotonic allocation scheme if the revenue function exhibits increasing returns to scale. Furthermore, it is shown that all superadditive games are deposit games if one allows for debt. |
| Keywords: | cooperative game theory;deposit games;core elements;population monotonic allocation schemes;superadditive games |
| JEL: | C71 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:200722&r=gth |
| By: | Eli Ben-Sasson; Adam Tauman Kalai; Ehud Kalai |
| Abstract: | A central question in game theory and artificial intelligence is how a rational agent should behave in a complex environment, given that it cannot perform unbounded computations. We study strategic aspects of this question by formulating a simple model of a game with additional costs (computational or otherwise) for each strategy. First we connect this to zero-sum games, proving a counter-intuitive generalization of the classic min-max theorem to zero-sum games with the addition of strategy costs. We then show that potential games with strategy costs remain potential games. Both zero-sum and potential games with strategy costs maintain a very appealing property: simple learning dynamics converge to equilibrium. |
| Keywords: | bounded rationality, zero sum games, potential games, strategic complexity. |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1439&r=gth |
| By: | Ehud Kalai |
| Abstract: | The sensitivity of Nash equilibrium to strategic and informational details presents a difficulty in applying it to games which are not fully speci?ed. Structurally-robust Nash equilibria are less sensitive to such details. More- over, they arrise naturally in important classes of games that have many semi- anonymous players. The paper describes this condition and its implications. |
| Keywords: | Nash equilibrium, ex-post Nash, structural robustness, metagames |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1403&r=gth |
| By: | Olivier Gossner; Jöhannes Horner |
| Abstract: | We study the relationship between a player’s (stage game) minmax payoff and the individually rational payoff in repeated games with imperfect monitoring. We characterize the signal structures under which these two payoffs coincide for any payoff matrix. Under a full rank assumption, we further show that, if the monitoring structure of an infinitely repeated game ‘nearly’ satisfies this condition, then these two payoffs are approximately equal, independently of the discount factor. This provides conditions under which existing folk theorems exactly characterize the limiting payoff set. |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1440&r=gth |
| By: | Peter Eso; James Schummer |
| Abstract: | In Sender-Receiver games with costly signaling, some equilibria are vulnerable to deviations which could be "unambiguously" interpreted by the Receiver as coming from a unique set of possible Sender-types. The vulnerability occurs when the types in this set are the ones who gain from the deviation, regardless of the posterior beliefs the Receiver forms over that set. We formalize this idea and use it to characterize a unique equilibrium outcome in two classes of games. First, in mono- tonic signaling games, only the Riley outcome is immune to this sort of deviation. Our result therefore provides a plausible story behind the selection made by Cho and Kreps' (1987) D1 criterion on this class of games. Second, we examine a version of Crawford and Sobel's (1982) model but with costly signaling and finite type sets, where standard refinements have no effect. We show that only a Riley-like separating equilibrium is immune to these deviations. |
| Keywords: | Signaling games, Sender-Receiver, robust equilibrium, re¯nements. |
| JEL: | C70 C72 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1406&r=gth |
| By: | Hongwei Gui; Rudolf M¨uller; Rakesh V. Vohra |
| Abstract: | This paper provides a characterization of dominant strategy mechanisms with quasi-linear utilities and multi-dimensional types for a variety of preference domains. These characterizations are in terms of a monotonicity property on the underlying allocation rule. |
| Keywords: | Dominant Strategy, Farkas Lemma, Combinatorial Auctions. |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1392&r=gth |
| By: | Alexey Malakhov; Rakesh V. Vohra |
| Abstract: | This paper highlights connections between the discrete and continuous approaches to optimal auction design with single and multi-dimensional types. We provide an interpretaion of an optimal auction design problem in terms of a linear program that is an instance of a parametric shortest path problem on a lattice. We also solve some cases explicitly in the discrete framework. |
| Keywords: | Auctions, Networks, Linear Programming |
| JEL: | C61 C70 D44 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1397&r=gth |
| By: | Stenger, Horst; Gabler, Siegfried; Schmidt, Jochen (Institut für Volkswirtschaft und Statistik (IVS)) |
| Abstract: | A linaer game consists of two subsets of a vector space with a scalar product. The idea is that players 1 and 2 select, independently, elements of the first an second set, respectively. Then, player 2 has to pay to player 1 the value of the scalar product of the selected elememts. We will discuss survey sampling within the framework of linear games with the statistician in the role of player 2. The vector space to be considered is the set of all symmetric matrices of order N x N with a scalar product identical with the usual mean squared error. The subset from with the statistician`s selection is to be made is neither convex nor compact. Standard results of the theory of linear games have to be modified appropriately. The existence of minimax strategies will be established. At the same time we hope to improve our understanding of random selection and of the duality between the fixed population approach and model based approaches to the theory of survey sampling. |
| URL: | http://d.repec.org/n?u=RePEc:mea:ivswpa:586&r=gth |
| By: | Thierry Bréchet (Université Catholique de Louvain); François Gerard (Center for Operations Research and Econometrics (CORE) and Université Catholique de Louvain) |
| Abstract: | Using an updated version of the CWS model (introduced by Eyckmans and Tulkens in Resource and Energy Economics 2003), this paper intends to evaluate with numbers the respective merits of two competing notions of coalition stability in the standard global public goods model as customarily applied to the climate change problem. After a reminder of the model structure and of the definition of the two game theoretical stability notions involved – namely, core stability and internal-external stability, the former property is shown to hold for the grand coalition in the CWS model only if resource transfers of a specific form between countries are introduced. It is further shown that while the latter property holds neither for the grand coalition nor for most large coalitions, it is nevertheless verified in a weak sense that involves transfers (dubbed “potential internal stability”) for most small coalitions. The reason for this difference is brought to light, namely the differing rationale that inspires the transfers in either case. Finally, it is shown that the stable coalitions that perform best (in terms of carbon concentration and global welfare) are always composed of both industrialized and developing countries. Two sensitivity analyses confirm the robustness of all these results. |
| Keywords: | Climate Change, Coalitions, Simulation, Integrated Assessment |
| JEL: | C71 C73 D9 D62 F42 Q2 |
| Date: | 2007–02 |
| URL: | http://d.repec.org/n?u=RePEc:fem:femwpa:2007.21&r=gth |
| By: | Johannes Horner; Julian Jamison |
| Abstract: | We study an infinitely-repeated ?rst-price auction with common values. Initially, bid- ders receive independent private signals about the objects' value, which itself does not change over time. Learning occurs only through observation of the bids. Under one-sided incomplete information, this information is eventually revealed and the seller extracts es- sentially the entire rent (for large discount factors). Both players?payo¤s tend to zero as the discount factor tends to one. However, the uninformed bidder does relatively better than the informed bidder. We discuss the case of two-sided incomplete information, and argue that, under a Markovian re?nement, the outcome is pooling: information is revealed only insofar as it does not affect prices. Bidders submit a common, low bid in the tradition of collusion without conspiracy. |
| Keywords: | repeated game with incomplete information; private information; ratchet effect; first-price auction; dynamic auctions |
| JEL: | C72 D44 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1422&r=gth |
| By: | Jacques Cremer; Yossi Spiegel; Charles Z. Zheng |
| Abstract: | We study the design of profit maximizing single unit auctions under the assumption that the seller needs to incur costs to contact prospective bidders and inform them about the auction. With independent bidders’ types and possibly interdependent valuations, the seller’s problem can be reduced to a search problem in which the surplus is measured in terms of virtual utilities minus search costs. Compared to the socially efficient mechanism, the optimal mechanism features fewer participants, longer search conditional on the same set of participants, and inefficient sequence of entry. |
| Keywords: | optimal auctions, search cost, search mechanism |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1421&r=gth |
| By: | JEFFREY C. ELY; MARCIN PESKI |
| Abstract: | In games with incomplete information, conventional hierarchies of belief are incomplete as descriptions of the players’ information for the purposes of determining a player’s behavior. We show by example that this is true for a variety of solution concepts. We then investigate what is essential about a player’s information to identify rationalizable behavior in any game. We do this by constructing the universal type space for rationalizability and characterizing the types in terms of their beliefs. Infinite hierarchies of beliefs over conditional beliefs, what we call delta-hierarchies, are what turn out to matter. We show that any two types in any two type spaces have the same rationalizable sets in all games if and only if they have the same delta-hierarchies. |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1388&r=gth |
| By: | Peters, Michael; Halevy, Yoram |
| Abstract: | The Ultimatum Game seems to be the ideal experiment to test the sequential rationality assumptions underlying subgame perfection. We illustrate with a simple example why this interpretation of the experimental results may be misguided. Instead, we approach the ultimatum game as a mechanism designed to elicit information about the preferences and beliefs of players. While remaining agnostic about the right way to interpret preferences, we maintain the assumption that preferences are interdependent - the utility of a player may be a function of other players types. We explain how to recast the best known explanations of the experimental evidence in these terms. We then illustrate how standard arguments can be used to extract the information conveyed by existing experimental results, and how the latter can restrict the set of plausible models of interdependence. |
| Date: | 2007–03–31 |
| URL: | http://d.repec.org/n?u=RePEc:ubc:pmicro:peters-07-03-31-11-46-48&r=gth |
| By: | Alp E. Atakan |
| Abstract: | This paper shows that all perfect Bayesian equilibria of a decentralized dynamic matching market with two-sided incomplete information of independent private values variety converge to competitive equilibria. Each buyer wants to purchase a bundle of heterogeneous, indivisible goods and each seller owns one unit of a heterogeneous indivisible good (as in Kelso and Crawford (1982) or Gul and Stacchetti (1999)). Buyer preferences and endowments as well as seller costs are private information. Agents engage in costly search and meet randomly. The terms of trade are determined through bilateral bargaining between buyers and sellers. The paper considers a market in steady state. It is shown that as frictions, i.e., discounting and fixed costs of search become small, all equilibria of the market game converge to perfectly competitive equilibria. |
| Keywords: | Bargaining, Search, Matching |
| JEL: | C73 C78 D83 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1437&r=gth |
| By: | Ehud Kalai |
| Abstract: | This is a draft of a chapter for a book called "Game Theory, 5 Questions," to be published by Automatic Pressed/VIP.Below are five questions and my answers. Any feedback is appreciated. |
| Keywords: | game theory, applications, game science, bounded rationality, behavioral game theory |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1426&r=gth |
| By: | Wolfgang Leininger; Axel Ockenfels |
| Abstract: | We document an increase in the scoring probability from penalties in soccer, which separates the time period before 1974 significantly from that after 1976: the scoring probability increased by 11%.We explain this finding by arguing that the institution of penalty-shooting before 1974 is best described as a standard of behaviour for striker and goal-keeper, which in game-theoretic terms represents a 2x2-game. In contrast to this, after 1976 the institution of the penalty-duel is best described by a 3x3 game form constrained by certain behavioural rules. Those rules can be parameterized by a single parameter, which nevertheless allows the theoretical reproduction (and hence explanation) of all the empirically documented regularities.The scoring probability in equilibrium of the latter institution is higher than in the former one.We present historical evidence to the effect, that this change in the perception of penalty- duels (as two different games), was caused by Johan Neeskens’ shrewd and “revolutionary” penalty-taking during World-Cup 1974, when he shot a penalty in the first minute of the final between Germany and the Netherlands right into the middle of the goalmouth. |
| Keywords: | Professional soccer, mixed strategy equilibrium, institutional design |
| JEL: | D01 C72 D74 C93 |
| Date: | 2007–03 |
| URL: | http://d.repec.org/n?u=RePEc:rwi:repape:0004&r=gth |
| By: | Daniel Houser; Daniel Schunk; Joachim Winter (Mannheim Research Institute for the Economics of Aging (MEA)) |
| Abstract: | The relationship between trust and risk is a topic of enduring interest. Although there are substantial differences between the ideas the terms express, many researchers from different disciplines have pointed out that these two concepts become very closely related in personal exchange contexts. This raises the important practical concern over whether behaviors in the widely-used “trust game” actually measure trust, or instead reveal more about risk attitudes. It is critical to confront this question rigorously, as data from these games are increasingly used to support conclusions from a wide variety of fields including macroeconomic development, social psychology and cultural anthropology. The aim of this paper is to provide cogent evidence on the relationship between trust and risk in “trust” games. Subjects in our experiment participate either in a trust game or in its risk game counterpart. In the trust version, subjects play a standard trust game and know their counterparts are human. In the risk version, subjects know their counterparts are computers making random decisions. We compare decisions between these treatments, and also correlate behavior with subjects’ risk attitudes as measured by the Holt and Laury (2002) risk instrument. We provide evidence that trusting behavior is different than behavior under risk. In particular, (i) decisions patterns in our trust and risk games are significantly different; and (ii) risk attitudes predict decisions in the risk game, but not the trust game. |
| Date: | 2006–12–31 |
| URL: | http://d.repec.org/n?u=RePEc:xrs:meawpa:06112&r=gth |
| By: | Eddie Dekel; Drew Fudenberg |
| Abstract: | We define and analyze a "strategic topology" on types in the Harsanyi-Mertens- Zamir universal type space, where two types are close if their strategic behavior is similar in all strategic situations. For a fixed game and action define the distance be- tween a pair of types as the di¤erence between the smallest " for which the action is " interim correlated rationalizable. We define a strategic topology in which a sequence of types converges if and only if this distance tends to zero for any action and game. Thus a sequence of types converges in the strategic topology if that smallest " does not jump either up or down in the limit. As applied to sequences, the upper-semicontinuity prop- erty is equivalent to convergence in the product topology, but the lower-semicontinuity property is a strictly stronger requirement, as shown by the electronic mail game. In the strategic topology, the set of "finite types" (types describable by finite type spaces) is dense but the set of finite common-prior types is not. |
| Keywords: | rationalizability, incomplete informa- tion, common knowledge, universal type space, strategic topology. |
| JEL: | C70 C72 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1417&r=gth |
| By: | Marco Pagnozzi (University of Napoli "Federico II" and CSEF) |
| Abstract: | The possibility of resale after an auction attracts speculators (i.e., bidders who have no use value for the objects on sale). In a multi-object auction, a high-value bidder may strictly prefer to let a speculator win some of the objects and then buy in the resale market, in order to keep the auction price low for the objects she wins in the auction. Therefore, although speculators increase competition in the auction, they also affect high-value bidders.incentives to .reduce demand..We show that the net e¤ect on the seller.s revenue of allowing resale to attract speculators depends on the heterogeneity of bidders.valuations. But the presence of speculators may increase the seller.s revenue only if speculators are eventually outbid. We also analyze the effect on the seller.s revenue of allowing resale in the absence of speculators, and we discuss the strategies that the seller can adopt to increase his revenue. |
| Keywords: | multi-object auctions, speculation, resale, demand reduction |
| JEL: | D44 |
| Date: | 2007–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:176&r=gth |
| By: | Alexey Malakhov; Rakesh V. Vohra |
| Abstract: | We consider an environment with a single divisible good and two bidders. The valuations of the bidders are private information but one bidder has a commonly known budget constraint. For this environment we derive the revenue maximizing subsidy free incentive compatible auction. We also examine the case when the budget constraint is private information but bidders must post a bond. |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1419&r=gth |
| By: | Copic, Jernej; Katz, Jonathan |
| Date: | 2007–03 |
| URL: | http://d.repec.org/n?u=RePEc:clt:sswopa:1266&r=gth |
| By: | Dritan Osmani; Richard S.J. Tol (Economic and Social Research Institute, Dublin) |
| Abstract: | Non-cooperative game theoretical models of self-enforcing international environmental agree- ments (IEAs) that employ the cartel stability concept of d'Aspremont et al. (1983) frequently use the assumption that countries can sign a single agreement only. We modify the assump- tion by considering two self-enforcing IEAs. Extending a model of Barrett (1994a) on a single self-enforcing IEA, we demonstrate that there are many similarities between one and two self- enforcing IEAs. But in the case of few countries and high environmental damage we show that two self-enforcing IEA work far better than one self-enforcing IEA in terms of both welfare and environmental equality |
| Keywords: | self-enforcing international environmental agreements, non-cooperative game theory, stability, nonlinear optimization. |
| JEL: | C61 C72 H41 |
| Date: | 2005–08 |
| URL: | http://d.repec.org/n?u=RePEc:sgc:wpaper:82&r=gth |
| By: | Johannes Horner; Dinah Rosenberg; Eilon Solan; Nicolas Vieille |
| Abstract: | We consider an example of a Markov game with lack of information on one side, that was first introduced by Renault (2002). We compute both the value and optimal strategies for a range of parameter values. |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1412&r=gth |
| By: | Philip Bond (Finance Department, The Wharton School, University of Pennsylvania); Hülya Eraslan (Finance Department, The Wharton School, University of Pennsylvania) |
| Abstract: | Prior research on “strategic voting” has reached the conclusion that unanimity rule is uniquely bad: it results in destruction of information, and hence makes voters worse off. We show that this conclusion depends critically on the assumption that the issue being voted on is exogenous, i.e., independent of the voting rule used. We depart from the existing literature by endogenizing the proposal that is put to a vote, and establish that under many circumstances unanimity rule makes voters better off. Moreover, in some cases unanimity rule also makes the proposing individual better off even when he has diametrically opposing preferences. In this case, unanimity is the Pareto dominant voting rule. Voters prefer unanimity rule because it induces the proposing individual to make a more attractive proposal. The proposing individual prefers unanimity rule because the acceptance probabilities for moderate proposals are higher. |
| Keywords: | Strategic voting; agenda setting; multilateral bargaining |
| JEL: | C7 D7 D8 |
| Date: | 2004–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:pen:papers:07-014&r=gth |
| By: | Jacques Cremer; Yossi Spiegel; Charles Z. Zheng |
| Abstract: | We consider auction environments in which bidders must incur a cost to learn their valuations and study the optimal selling mechanisms in such environments. These mechanisms specify for each period, as a function of the bids in previous periods, which new potential buyers should be asked to bid. In addition, these mechanisms must induce buyers to both acquire and to reveal truthfully their valuations. Using a generalized Groves principle, we prove a very general “full extraction of the surplus” result: the seller can obtain the same profit as if he had full control over the buyers’ acquisition of information and could have observed directly their valuations once they are informed. We also present appealing implementations of the optimal mechanism in special cases. |
| Keywords: | mechanism design, selling mechanisms, auctions, information acquisition, search procedures |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1420&r=gth |
| By: | Spichtig, Mathias; Traxler, Christian |
| Abstract: | This paper develops a model of social norms and cooperation in large societies. Within this framework we use an indirect evolutionary approach to study the endogenous formation of preferences and the coevolution of norm compliance. Thereby we link the multiplicity of equilibria, which emerges in the presence of social norms, to the evolutionary analysis: Individuals face situations where many others cooperate as well as situations where a majority free-rides. The evolutionary adaptation to such heterogenous environments will favor conditional cooperators, who condition their pro-social behavior on the others' cooperation. As conditional cooperators react flexibly to their social environment, they dominate free-riders as well as unconditional cooperators. |
| Keywords: | Conditional Cooperation; Indirect Evolution; Social Norms; Heterogenous Environments |
| JEL: | C70 Z13 |
| Date: | 2007–03 |
| URL: | http://d.repec.org/n?u=RePEc:lmu:muenec:1398&r=gth |