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on Game Theory |
| By: | Ana Espinola-Arredondo; Felix Munoz-Garcia (School of Economic Sciences, Washington State University) |
| Abstract: | Recent experimental evidence supports the in?uence of a player?s unchosen alternatives in other agent?s actions. This paper examines a tractable theoretical model of reference-dependent preferences in which individuals compare other players?chosen action with respect to their un- chosen alternatives. We analyze the equilibrium prediction in complete information sequential- move games, and compare it with that of standard games where players are not concerned about unchosen alternatives. We show that, without relying on interpersonal payo¤ comparisons (i.e., with strictly individualistic agents), our model predicts higher cooperation among the players than standard game-theoretic models. In addition, our framework embodies certain behavioral models from the literature on social status acquisition and intentions-based reciprocity as spe- cial cases. Finally, we con?rm our results in three economic applications: the labor market gift exchange game, the ultimatum bargaining game, and the sequential public good game. |
| Keywords: | Unchosen alternatives, Sequential-move games, Relative comparisons, Kindness, Reciprocity. |
| JEL: | C72 C78 C91 |
| Date: | 2008–08 |
| URL: | http://d.repec.org/n?u=RePEc:wsu:wpaper:espinola-2&r=gth |
| By: | John Duffy (University of Pittsburgh); Huan Xie (Concordia University); Yong-Ju Lee (Samsung Research Institute of Finance) |
| Abstract: | How do norms of trust and reciprocity arise? We investigate this question by examining behavior in an experiment where subjects play a series of indefinitely repeated trust games. Players are randomly and anonymously matched each period. The parameters of the game are chosen to support trust and reciprocity as a sequential equilibrium when no reputational information is available. The main question addressed is whether a social norm of trust and reciprocity emerges under the most extreme information restriction (community-wide enforcement) or whether trust and reciprocity require additional, individual-specific information about a player's past history of play. In the absence of such reputational information, we find that a social norm of trust and reciprocity is difficult to sustain. The provision of reputational information on past individual decisions significantly increases trust and reciprocity when subjects have experienced the absence of such a mechanism. Importantly, we find that making reputational information available at a small cost may also lead to a significant improvement in trust and reciprocity, despite the fact that most subjects do not choose to purchase this information. |
| Keywords: | Social Norms, Trust Game, Random Matching, Trust and Reciprocity, Information, Reputational Information |
| JEL: | C72 C91 C92 |
| Date: | 2008–10 |
| URL: | http://d.repec.org/n?u=RePEc:crd:wpaper:08007&r=gth |
| By: | Felix Munoz-Garcia (School of Economic Sciences, Washington State University) |
| Abstract: | This paper analyzes the e¤ects of players? relative comparisons in complete information simultaneous-move games. In particular, every individual is assumed to evaluate the kindness she infers from other players?choices by comparing these choices with respect to a given refer- ence level. Speci?cally, this paper identi?es under what conditions the introduction of relative comparisons leads players to be more cooperative than in standard game-theoretic models. I show that this result holds under certain conditions on the speci?c reference point that players use in their relative comparisons, and on whether players?relative comparisons leads them to regard each others? actions as more strategic complementary or substitutable. The model is then applied to di¤erent examples in public good games which enhance the intuition behind the results. Finally, I show that some existing models in the literature of intentions-based reciprocity and social status acquisition can be rationalized as special cases. |
| Keywords: | Relative comparisons, Reference points, Simultaneous-move games, Kindness, Strategic complementarities. |
| JEL: | C72 C78 C91 |
| Date: | 2008–08 |
| URL: | http://d.repec.org/n?u=RePEc:wsu:wpaper:munoz-1&r=gth |
| By: | Kirchkamp Oliver; Reiss J. Philipp; Sadrieh Abdolkarim (METEOR) |
| Abstract: | We introduce a new method of varying risk that bidders face in first-price and second-price private value auctions. We find that decreasing bidders’ risk in first-price auction reduces the degree of overbidding relative to the risk-neutral Bayesian Nash equilibrium prediction.This finding is consistent with the risk-aversion explanation of overbidding. Furthermore, we apply the method to second-price auctions and find that bidding behavior is robust to manipulating bidders'' risk as generally expected in auction theory. |
| Keywords: | microeconomics ; |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2008050&r=gth |
| By: | Manuela A. D. Aguiar (Faculdade de Economia, Universidade do Porto); Sofia B. S. D. Castro (Faculdade de Economia, Universidade do Porto) |
| Abstract: | We study robust long-term complex behaviour in the Rock-Scissors-Paper game with two players, played using reinforcement learning. The complex behaviour is connected to the existence of a heteroclinic network for the dynamics. This network is made of three heteroclinic cycles consisting of nine equilibria and the trajectories connecting them. We provide analytical proof both for the existence of chaotic switching near the heteroclinic network and for the relative asymptotic stability of at least one cycle in the network, leading to behaviour ranging from almost deterministic actions to chaotic-like dynamics. Our results are obtained by making use of the symmetry of the original problem, a new approach in the context of learning. |
| Keywords: | learning process, dynamics, switching, chaos |
| JEL: | C72 D83 |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:por:fepwps:305&r=gth |
| By: | Eugen Kovac; Jakub Steiner |
| Abstract: | Agents at the beginning of a dynamic coordination process (1) are uncertain about actions of their fellow players and (2) anticipate receiving strategically relevant information later on in the process. In such environments, the irreversibility of early actions plays an important role in the choice among them. We characterize the strategic effects of the reversibility option on the coordination outcome. Such an option can either enhance or hamper efficient coordination, and we determine the direction of the effect based only on simple features of the coordination problem. The analysis is based on a generalization of the Laplacian property known from static global games: players at the beginning of a dynamic game act as if they were entirely uninformed about aggregate play of fellow players in each stage of the coordination process. |
| Keywords: | : Delay, Exit, Global Games, Laplacian Belief, Learning, Option, Reversibility. |
| JEL: | C7 D8 |
| Date: | 2008–07–16 |
| URL: | http://d.repec.org/n?u=RePEc:edn:esedps:183&r=gth |
| By: | Joseph Abdou (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris) |
| Abstract: | An interaction form is an abstract model of interaction based on a description of power distribution among agents over alternatives. A solution known as the settlement set is defined at any preference profile. Necessary and sufficient conditions for stability, that is the existence of settlements, are established. A Stability Index that plays a role similar to that of the Naka- mura Number is defined. It measures, loosely speaking, the complexity of those configurations that prevent a settlement. To any strategic game form one can associate an interaction form in such a way that given an equilibrium concept (e.g. Nash or strong Nash) and a preference profile, settlements of the interaction form are precisely the equilibrium outcomes of the resulting game. As a consequence we have necessary and sufficient conditions for the solvability of game forms. The paper provides a localization of the index in case of unstability. |
| Keywords: | Interactive Form, Stability Index, Nash Equilibrium, Strong Equilibrium, Solvability, Consistency, Simple Game, Effectivity Function, Acyclicity, Nakamura Number. |
| Date: | 2008–12–15 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-00347438_v1&r=gth |
| By: | Mengel Friederike (METEOR) |
| Abstract: | We present a model of adaptive economic agents that are k periods forward looking. Agents in our model are randomly matched to interact in finitely repeated games. They form beliefs by relying on their past experience in the same situation (after the same recent history) and then best respond to these beliefs looking k periods ahead. We establish almost sure convergence of our stochastic process and characterize absorbing sets. These can be very different from the predictions in both the fully rational model and the adaptive, but myopic case. In particular we find that also Non-Nash outcomes can be sustained almost all the time whenever they are individually rational and satisfy an efficiency condition. We then characterize stochastically stable states in 2×2 games and show that under certain conditions the efficient action in Prisoner''s Dilemma games and Coordination games can be singled out as uniquely stochastically stable. We show that our results are consistent with typical patterns observed in experiments on finitely repeated Prisoner''s Dilemma games. Finally, if populations are composed of some myopic and some forward looking agents parameter constellations exists such that either might obtain higher average payoffs. |
| Keywords: | Economics (Jel: A) |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:umamet:2008053&r=gth |
| By: | Daijiro Okada (Department of Economics, Rutgers, The State University of New Jersey); Olivier Tercieux (Paris School of Economics and CNRS) |
| Abstract: | We show that local potential maximizer ([15]) with constant weights is stochas- tically stable in the log-linear dynamics provided that the payo® function or the associated local potential function is supermodular. We illustrate and discuss, through a series of examples, the use of our main results as well as other concepts closely related to local potential maximizer: weighted potential maximizer, p- dominance. We also discuss the log-linear processes where each player's stochastic choice rule converges to the best response rule at di®erent rates. For 2£2 games, we examine a modi¯ed log-linear dynamics (relative log-linear dynamics) under which local potential maximizer with strictly positive weights is stochastically sta- ble. This in particular implies that for 2 £ 2 games a strict (p1; p2)-dominant equilibrium with p1 + p2 < 1 is stochastically stable under the new dynamics. |
| Keywords: | Log-linear dynamics, Relative log-linear dynamics, Stochastic stability, local potential maximizer, p-dominant equilibrium, equilibrium selection, stochastic order, comparison of Markov chains |
| JEL: | C72 C73 |
| Date: | 2008–11 |
| URL: | http://d.repec.org/n?u=RePEc:ads:wpaper:0085&r=gth |
| By: | Yingyao Hu; Matthew Shum |
| Abstract: | In this paper we consider the nonparametric identification of Markov dynamic games models in which each firm has its own unobserved state variable, which is persistent over time. This class of models includes most models in the Ericson and Pakes (1995) and Pakes and McGuire (1994) framework. We provide conditions under which the joint Markov equilibrium process of the firms' observed and unobserved variables can be nonparametrically identified from data. For stationary continuous action games, we show that only three observations of the observed component are required to identify the equilibrium Markov process of the dynamic game. When agents?choice variables are discrete, but the unobserved state variables are continuous, four observations are required. |
| Date: | 2008–10 |
| URL: | http://d.repec.org/n?u=RePEc:jhu:papers:546&r=gth |
| By: | Eric Maskin (Institute for Advanced Study, School of Social Science) |
| Keywords: | Nash, mechanism design |
| Date: | 2008–11 |
| URL: | http://d.repec.org/n?u=RePEc:ads:wpaper:0086&r=gth |
| By: | Thomas Tröger; Rodney Garratt; Charles Zheng |
| Abstract: | The English auction is susceptible to tacit collusion when post-auction inter-bidder resale is allowed. We show this by constructing equilibria where, with positive probability, one bidder wins the auction without any competition and divides the spoils by optimally reselling the good to the other bidders. These equilibria interim Pareto dominate (among bidders) the standard value-bidding equilibrium, without requiring the bidders to make any commitment on bidding behavior or post-bidding spoil-division. |
| Keywords: | English auction, resale, collusion |
| JEL: | D44 |
| Date: | 2008–10 |
| URL: | http://d.repec.org/n?u=RePEc:bon:bonedp:bgse20_2008&r=gth |
| By: | Bernard Lebrun (York University, Toronto) |
| Abstract: | In the independent-private-value model, we allow resale among bidders following a first-price sealed-bid, second-price sealed-bid, or English auction with two bidders. We consider two regimes with regard to the disclosure of the sealed bids: full disclosure and no disclosure. Either the auction winner or the auction loser chooses the resale mechanism. Thanks to three key properties our model shares with the common-value model, we obtain explicit formulas for the equilibria. We circumvent the “ratchet effect,” by “randomizing” every pure equilibrium under no disclosure into an equivalent behavioral equilibrium under full disclosure. We compare the auctioneer’s revenues across auctions and bargaining procedures. We present some nbidder extensions. |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:yca:wpaper:2008_06&r=gth |
| By: | Robert S. Gazzale (Williams College); Tapan Khopkar |
| Abstract: | By providing incentives for sellers to act in a trustworthy manner, reputation mechanisms in many online environments can mitigate moral-hazard problems when particular buyers and sellers interact infrequently. However, these mechanisms rely on buyers sharing their private information about sellers with the community, and thus may suffer from too little feedback when its provision is costly. In this experimental study, we compare a standard feedback mechanism to one in which sellers can inspect a buyer's feedback-provision history, thus providing the buyer with incentives to share private information even when costly. We find fairly high trust and trustworthiness levels in all markets, with buyers showing a willingness to provide costly feedback, especially negative feedback, sufficient to induce seller trustworthiness. While we find, ceteris paribus, evidence that the availability of feedback-provision histories increases buyer trust by reducing missing feedback, it did not improve overall trustworthiness as this information enabled sellers to discriminate and act in a trustworthy manner less frequently with those who share information less frequently. |
| Keywords: | experimental economics, trust, reputation, electronic markets |
| JEL: | C72 C73 C91 C92 D82 L14 |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:wil:wileco:2008-22&r=gth |
| By: | Dockner, E.J. (University of Vienna); Wagener, F.O.O. (Universiteit van Amsterdam) |
| Abstract: | Many economic problems can be formulated as dynamic games in which strategically interacting agents choose actions that determine the current and future levels of a single capital stock. We study necessary conditions that allow us to characterise Markov perfect Nash equilibria for these games. These conditions result in an auxiliary system of ordinary differential equations that helps us to explore stability, continuity and differentiability of these equilibria. The techniques are used to derive detailed properties of Markov-perfect Nash equilibria for several games including the exploitation of a finite resource, the voluntary investment in a public capital stock, and the inter-temporal consumption of a reproductive asset. |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:ams:ndfwpp:08-09&r=gth |
| By: | Matthias Sutter; Ronald Bosman; Martin Kocher; Frans van Winden |
| Abstract: | We study the influence of gender and gender pairing on economic decision making in an experimental two-person bargaining game where the other party’s gender is known to both actors. We find that (1) gender per se has no significant effect on behavior, whereas (2) gender pairing systematically affects behavior. In particular, we observe much more competition and retaliation and, thus, lower efficiency when the bargaining partners have the same gender than when they have the opposite gender. These findings are consistent with predictions from psychology. Implications of our results for real-world organizations are discussed. |
| Keywords: | gender pairing, bargaining, psychology, experiment |
| JEL: | C72 C91 C92 |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:inn:wpaper:2008-27&r=gth |
| By: | Ángel Hernando Veciana (Universidad de Alicante); Fabio Michelucci (California Institute of Technology) |
| Abstract: | We characterize the incentive compatible allocation that maximizes the expected social surplus in a single-unit sale when the efficient allocation is not implementable. This allocation may involve no selling when it is efficient to sell. We then show that the English auction always implements the second best allocation when there are only two bidders, but not with more than two. Our model employs a unidimensional type space with independent types and allocative externalities, but captures some features of models with multidimensional types. |
| Keywords: | Efficiency, auctions, mechanism design |
| JEL: | D44 D82 |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:ivi:wpasad:2008-17&r=gth |
| By: | Susan Athey; Jonathan Levin; Enrique Seira |
| Abstract: | We study entry and bidding patterns in sealed bid and open auctions with heterogeneous bidders. Using data from U.S. Forest Service timber auctions, we document a set of systematic effects of auction format: sealed bid auctions attract more small bidders, shift the allocation towards these bidders, and can also generate higher revenue. We show that a private value auction model with endogenous participation can account for these qualitative effects of auction format. We estimate the model's parameters and show that it can explain the quantitative effects as well. Finally, we use the model to provide an assessment of bidder competitiveness, which has important consequences for auction choice. |
| JEL: | D44 D82 L13 L40 |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:14590&r=gth |
| By: | Itai Sher (Department of Economics, University of Minnesota) |
| Abstract: | This paper studies shill bidding in the VCG mechanism applied to combinatorial auc- tions. Shill bidding is a strategy whereby a single decision-maker enters the auction under the guise of multiple identities. I characterize the optimal shill bidding strategy given that the decision-maker knows or has correctly guessed the aggregate bid of her opponents. The optimization problem is decomposed into two parts: (i) for any package B, nd the cheapest way to win B using shills, and (ii) select the package that max- imizes utility given that it is won in the cheapest way. The analysis of (i) shows how shill bidding reduces prices in the VCG mechanism and thereby provides an incentive to shill. The optimal shill bidding strategy has the characteristic that dierent shills sponsored by the same decision-maker do not compete with one another. The char- acterization of optimal sill bidding leads to an exact characterization of the aggregate bids b in the VCG mechanism such that some bidder would have an incentive to shill bid against b. As has been found by related studies, when goods are substitutes, there is no incentive to shill bid. In contrast, this paper shows that when goods are pure complements, the incentive to shill takes a simple form: there is an incentive to disin- tegrate and bid for each item using a dierent identity. With a mix of substitutes and complements, the problem is computationally hard; in particular, nding the optimal shill bidding strategy is equivalent to nding an ecient allocation in a combinatorial auction{the so called winner determination problem. Shill bidding is closely related to collusion. Setting aside the ordinary incentive to suppress competition, the disincentive to disintegrate using shills when facing a substitutes valuation is shown to translate into an incentive to merge for a coalition facing the same valuation. Only when valuations are additive can the incentives to shill and merge simultaneously disappear. The paper also shows that there does not exist a dominant strategy in the VCG mechanism when shill bidding is possible. I nd a large class of shill bidding strategies which sometimes outperform truthful bidding, but also show that no shill bidding strategy dominates truthful bidding. |
| Keywords: | VCG mechanism, combinatorial auctions, winner determination problem, collusion. |
| JEL: | C72 D44 |
| Date: | 2008–12–29 |
| URL: | http://d.repec.org/n?u=RePEc:min:wpaper:2008-4&r=gth |
| By: | Attila Ambrus; Kareen Rozen |
| Date: | 2008–12–26 |
| URL: | http://d.repec.org/n?u=RePEc:cla:levarc:122247000000002161&r=gth |
| By: | Huan Xie (Concordia University) |
| Abstract: | This paper studies a bargaining model in which the seller is uncertain about which distribution the buyer's values are drawn from. The distribution of the buyer's values is fixed across periods, while the buyer's values are drawn independently from the distribution each period. In the classical model of repeated bargaining where the buyer's value is drawn from a commonly known distribution and fixed across periods, the high-value buyer has a strong incentive to conceal his value, and the seller loses most of her bargaining power. An important question is whether adding a layer of uncertainty makes the high-value buyer more willing to accept high-price offers and improves the seller's revenue. We find this to be the case as long as the seller's ex ante beliefs are sufficiently optimistic. |
| Keywords: | Repeated Bargaining, Uncertain Value Distributions, Revenue Comparison, Learning |
| JEL: | C73 D81 D82 |
| Date: | 2008–07 |
| URL: | http://d.repec.org/n?u=RePEc:crd:wpaper:08005&r=gth |
| By: | Polachek, Solomon (Binghamton University, New York); Xiang, Jun (University of Rochester) |
| Abstract: | This paper shows that the opportunity costs resulting from economic interdependence decrease the equilibrium probability of war in an incomplete information game. This result is strongly consistent with existing empirical analyses of the inverse trade-conflict relationship, but is the opposite of the conclusion reached by Gartzke et al. (2001), who reject the opportunity cost argument in a game-theoretic framework. As a result of this paper's findings, one cannot dismiss the opportunity cost argument as the explanation why trading nations fight less. Instead this study reaffirms the central position of opportunity costs as the basis for the inverse trade-conflict relationship, thus implying that one need not rely on signaling. |
| Keywords: | war, conflict, trade, trade-conflict relationship, interdependence, incomplete information game, signaling |
| JEL: | F10 C7 P16 |
| Date: | 2008–12 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp3883&r=gth |
| By: | Bettina Klaus (Harvard Business School, Negotiation, Organizations & Markets Unit) |
| Abstract: | We consider one-to-one matching markets in which agents can either be matched as pairs or remain single. In these so-called roommate markets agents are consumers and resources at the same time. We investigate two new properties that capture the effect a newcomer has on incumbent agents. Competition sensitivity focuses on the newcomer as additional consumer and requires that some incumbents will suffer if competition is caused by a newcomer. Resource sensitivity focuses on the newcomer as additional resource and requires that this is beneficial for some incumbents. For solvable roommate markets, we provide the first characterizations of the core using either competition or resource sensitivity. On the domain of all roommate markets, we obtain two associated impossibility results. |
| Keywords: | Core, Matching, Competition Sensitivity, Resource Sensitivity, Roommate Market. |
| JEL: | C78 D63 |
| Date: | 2007–11 |
| URL: | http://d.repec.org/n?u=RePEc:hbs:wpaper:09-072&r=gth |