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on Game Theory |
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Issue of 2013‒11‒29
twenty-two papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Joosung Lee |
| Abstract: | I introduce a noncooperative coalitional bargaining model for characteristic function form games. A player not only buys out other players' resources and rights with upfront transfers as in Gul (Econometrica, 1989), but also strategically chooses partners instead of bargaining with a randomly selected opponent. Such transactions among players are interpreted as coalition formation. The main theorem provides a general inefficiency result. If a characteristic function form game has a strict subcoalition with a strictly positive worth and a player with a strictly positive marginal contribution to the grand-coalition, then an efficient stationary subgame perfect equilibrium does not exist, as long as the discount factor is sufficiently high but strictly less than 1. Two special results are established. A grand-coalition equilibrium is impossible when players are sufficiently patient, unless the characteristic function form game is a unanimity game. For a simple game with a veto player and multiple winning coalitions, a non-minimal winning coalition is formed with positive probability. In two applications, I study players' strategic alliance behavior and the effect of the strategic behavior on inequality. First, for three-player simple games, the equilibrium payoff vector Lorenz-dominates both the Shapley-Shubik power index and the core-constrained Nash bargaining solution. Second, for wage bargaining games, workers endogenously form a union and their equilibrium payoffs can be greater than marginal products. |
| JEL: | C72 C78 D72 D74 |
| Date: | 2013–11–20 |
| URL: | http://d.repec.org/n?u=RePEc:jmp:jm2013:ple701&r=gth |
| By: | Giménez-Gómez, José-Manuel; Vilella Bach, Misericòrdia |
| Abstract: | In this paper we prove that the Mas-Colell bargaining set coincides with the core for three-player balanced and superadditive cooperative games. This is no longer true without the superadditivity condition or for games with more than three-players. Furthermore, under the same assumptions, the coincidence between the Mas-Collel and the individual rational bargaining set (Vohra (1991)) is revealed. Keywords: Cooperative game, Mas-Colell bargaining set, balancedness, individual rational bargaining set. JEL classi fication: C71, D63, D71. |
| Keywords: | Jocs cooperatius, Economia del benestar, Elecció social, 33 - Economia, |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:urv:wpaper:2072/220221&r=gth |
| By: | Christian Ewerhart; Federico Quartieri |
| Abstract: | Szidarovszky and Okuguchi (Games and Economic Behavior, 1997) have provided useful conditions for the existence of a unique purestrategy Nash equilibrium in rent-seeking games of complete information. In this paper, we generalize their results to contests with incomplete information. Two assumptions are imposed on the information structure. First, the players?' valuations of winning are assumed to be multiplicatively separable (which includes the polar cases of private values and pure common value). Second, it is assumed that a player is never certain to be the only one with a positive budget. It is also shown that, unless the budgets of all players are zero in all states, at least two players realize a positive expected net rent. |
| Keywords: | Contests, equilibrium existence and uniqueness, incomplete information, rent dissipation |
| JEL: | D72 C72 |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:133&r=gth |
| By: | Sergio Currarini (University of Leicester, Universita' di Venezia and Euro-Mediterranean Center on Climate Change); Marco A. Marini (Department of Computer, Control and Management Engineering, Universita' degli Studi di Roma "La Sapienza") |
| Abstract: | In this paper we review a number of coalitional solution concepts for the analysis of cartel and merger stability in oligopoly. We show that, although so far the industrial organization and the cooperative game-theoretic literature have proceeded somehow independently on this topic, the two approaches are highly inter-connected. We first consider the basic problem of the stability of the whole industry association of firms under oligopoly and, for this purpose, we introduce the concept of core in oligopoly games. We show that different assumptions on the behaviour as well as on the timing of the coalitions of firms yield very different results on the set of allocations which are core-stable. We then consider the stability of associations of firms organized in coalition structures different from the grand coalition. To this end, various coalition formation games recently introduced by the so called endogenous coalition formation literature are critically reviewed. Again, different assumptions concerning the timing and the behaviour of firms are shown to yield a wide range of different results. We conclude by reviewing some recent extensions of the coalitional analysis to oligopolistic markets with heterogeneous firms and incomplete information. |
| Keywords: | Cooperative Games, Coalitions, Mergers, Cartels, Core, Games with Ex- ternalities, Endogenous Coalition Formation |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:aeg:report:2013-15&r=gth |
| By: | Gadea-Blanco, Pedro; Giménez-Gómez, José-Manuel; Marco-Gil, María del Carmen |
| Abstract: | It is well known that, in distributions problems, fairness rarely leads to a single viewpoint (see, for instance, Young (1994)). In this context, this paper provides interesting bases that support the simple and commonly observed behavior of reaching intermediate agreements when two prominent distribution proposals highlight a discrepancy in sharing resources. Specifi cally, we formalize such a conflicting situation by associating it with a `natural' cooperative game, called bifocal distribution game, to show that both the Nucleolus (Schmeidler (1969)) and the Shapley value (Shapley (1953a)) agree on recommending the average of the two focal proposals. Furthermore, we analyze the interpretation of the previous result by means of axiomatic arguments. Keywords: Distribution problems, Cooperative games, Axiomatic analysis, Nucleolus, Shapley value. JEL Classi fication Numbers: C71, D63, D71. |
| Keywords: | Jocs cooperatius, Economia del benestar, Elecció social, 33 - Economia, |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:urv:wpaper:2072/220217&r=gth |
| By: | Vesperoni, Alberto (University of Siegen) |
| Abstract: | A contest is a game where several players compete for winning prizes by expending costly efforts. We assume that the outcome of a contest is an ordered partition of the set of players (a ranking) and a contest success function assigns a probability to each possible outcome as a function of players’ efforts. We define a contest success function for contests whose outcome is a ranking of any type, i.e., with any number of players at each rank. This approach is new in contest theory since the axiomatic work has exclusively been on contests with single-winner, whose outcome is a ranking with one player in the first rank and all other players in the second rank. The contest success function is characterized by pair-swap consistency, which is an axiom of independence of irrelevant alternatives and generalizes the main axiom in Skaperdas (1996). |
| Keywords: | conflict; contest; ranking; success function; axiom; probabilistic choice |
| JEL: | C25 C70 D72 D74 D81 |
| Date: | 2013–11–25 |
| URL: | http://d.repec.org/n?u=RePEc:ris:nepswp:2013_008&r=gth |
| By: | Nejat Anbarci; Nick Feltovich; Mehmet Y. Gurdal |
| Abstract: | We introduce the contractor game , related to the ultimatum game (UG). The proposer makes an offer , and simultaneously sends a cheap talk message , indicating (possibly falsely) the amount of the offer. The responder observes the message with certainty and the offer with probability p before accepting or rejecting the offer. We theoretically examine versions with p = 0 and p = 0.5 along with the UG, played by some standard economic agents and others who are averse to inequity, lies and lying. The equilibria yield intuitive predictions, which are supported by our experimental results. Offers are higher when they might be seen by the responder. Messages over–state offers, but less so when the offer might be seen. Responders are more likely to accept an unseen offer if it might have been seen. When offers are seen, responders reward truthful messages, rather than punishing lies, compared to when no message is sent. |
| Keywords: | ultimatum game, messages, lies, truth–telling, other–regarding behaviour |
| JEL: | C72 C78 D82 |
| Date: | 2013–11–20 |
| URL: | http://d.repec.org/n?u=RePEc:dkn:econwp:eco_2013_7&r=gth |
| By: | Ezra Einy (BGU); Ori Haimanko (BGU); Ram Orzach (Oakland University, Rochester, MI 48309, USA); Aner Sela (BGU) |
| Abstract: | We study two-player common-value all-pay auctions in which the players have ex-ante asymmetric information represented by finite partitions of the set of possible values of winning. We consider two families of such auctions: in the first, one of the players has an information advantage (henceforth, IA) over his opponent, and in the second, no player has an IA over his opponent. We show that there exists a unique equilibrium in auctions with IA and explicitly characterize it; for auctions without IA we find a sufficient condition for the existence of equilibrium in monotonic strategies. We further show that, with or without IA, the ex-ante distribution of equilibrium effort is the same for every player (and hence the players' expected efforts are equal), although their expected payoffs are different. In auctions with IA, the players have the same ex-ante probability of winning, which is not the case in auctions without IA. |
| Keywords: | Common-value all-pay auctions, asymmetric information, information advantage |
| JEL: | C72 D44 D82 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:bgu:wpaper:1306&r=gth |
| By: | Kalyan Chatterjee (Department of Economics, Pennsylvania State University.); Kaustav Das (Department of Economics, University of Exeter) |
| Abstract: | We study a model of decentralised bilateral interactions in a small market where one of the sellers has private information about her value. There are two identical buyers and another seller, whose valuation is commonly known to be in between the two possible valuations of the informed seller. We consider two in?nite horizon games, with public and private simultaneous one-sided o¤ers respectively and simultaneous responses. We show that there is a stationary perfect Bayes?equilibrium for both models such that prices in all transactions converge to the same value as the discount factor goes to 1. |
| Keywords: | Bilateral Bargaining, Incomplete information, Outside options, Coase conjecture. |
| JEL: | C78 D82 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:exe:wpaper:1313&r=gth |
| By: | Marco Faillo; Alessandra Smerilli; Robert Sugden |
| Abstract: | Level-k and team reasoning theories, among others, have been used to explain experimental evidence on coordination games. Both theories succeed in explaining some results and both fail in explaining other results. Sometimes it is impossible to discriminate between them. For this reason we propose an experiment with pie games, similar to the ones used by Crawford et al. (2008). We observe subjects playing a series of coordination games, with different configurations of equality and Pareto-dominance, for which it is possible to provide clear predictions derived from both team reasoning and a particular cognitive hierarchy model: level-k theory. In line with previous experimental results, we find that each theory fails to predict observed behaviour in some games. However, because of the design of our experiment, we can go deeper into the matter. Our results show that Pareto dominance, fairness and uniqueness are good predictors for coordination choices. Secondly, we find mixed evidence about level-k and team reasoning theories. In particular team reasoning theory fails to predict choices when they picks out a solution which is Pareto dominated and not compensated by grater equality; Level-k theory fails in games in which it predicts the choice of one of not unique slices, and the unique choice is more equal than the alternative choices. This could represent a step forward to investigate the presence of team reasoning or level-k in coordinating behaviour |
| Keywords: | Coordination games, Focal points, Team reasoning, Level-k theory |
| JEL: | C72 C91 A13 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:trn:utwpce:1306&r=gth |
| By: | Andreas Blume; Ernest K. Lai; Wooyoung Lim |
| Abstract: | The paper formalizes Warner's (1965) randomized response technique (RRT) as a game and implements it experimentally, thus linking game theoretic approaches to randomness in communication with survey practice in the field and a novel implementation in the lab. As predicted by our model and in line with Warner, the frequency of truthful responses is significantly higher with randomization than without. The model predicts that randomization weakly improves information elicitation, as measured in terms of mutual information, although, surprisingly, not always by RRT inducing truth-telling. Contrary to this prediction, randomization significantly reduces the elicited information in our experiment. |
| Keywords: | Randomized Response, Lying Aversion, Stigmatization Aversion, Mutual Information, Laboratory Experiments |
| JEL: | C72 C92 D82 D83 |
| Date: | 2013–07 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:490&r=gth |
| By: | Ansink, Erik; Weikard, Hans-Peter |
| Abstract: | In a river claims problem, agents are ordered linearly, and they have both an initial water endowment as well as a claim to the total water resource. We provide characterizations of two solutions to this problem, using Composition properties which have particularly relevant interpretations for the river claims problem. Specifically, these properties relate to situations where river flow is uncertain or highly variable, possibly due to climate change impacts. The only solution that satisfies all Composition properties is the `Harmon rule' induced by the Harmon Doctrine, which says that agents are free to use any water available on their territory, without concern for downstream impacts. The other solution that we assess is the `No-harm rule', an extreme interpretation of the no-harm principle from international water law, which implies that water is allocated as far downstream as possible. In addition to characterizing both solutions, we show their relation to priority rules and sequential sharing rules. |
| Keywords: | river claims problem; sharing rule; Harmon Doctrine; composition axioms; water allocation |
| JEL: | C71 D63 Q25 |
| Date: | 2013–11–20 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:51618&r=gth |
| By: | Nejat Anbarci; Pedro Gomis-Porqueras; Marcus Pivato |
| Abstract: | In formal markets, to attract buyers, sellers must publicly advertise their prices and locations. But in informal markets, sellers must remain anonymous from government authorities. Since agents' payoffs depend on the ratio of buyers and sellers in each of these markets, all agents try to position themselves in the market which can yield them the highest possible payoff. This strategic interaction in turn critically affects the time evolution of these two markets. In our benchmark model, in which only sellers can switch between these markets, there exists a unique stable dynamic equilibrium where formal and informal markets co-exist. Sellers switch from the formal to the informal market whenever costs of trading in the informal market decrease, and vice versa. In a richer environment, where both sellers and buyers can switch between markets, and the sellers' and buyers' costs of trading in the formal market net of those in the informal market have opposite signs, there exists a unique stable dynamic equilibrium where formal and informal markets co-exist. |
| Keywords: | Price posting, bargaining, matching, formal sector, informal sector |
| JEL: | C7 D49 |
| Date: | 2013–11–20 |
| URL: | http://d.repec.org/n?u=RePEc:dkn:econwp:eco_2013_6&r=gth |
| By: | Itai Arieli; Robert J. Aumann |
| Abstract: | The logic of backward induction (BI) in perfect information (PI) games has been intensely scrutinized for the past quarter century. A major development came in 2002, when P. Battigalli and M. Sinischalchi (BS) showed that an outcome of a PI game is consistent with common strong belief of utility maximization if and only if it is the BI outcome. Both BS's formulation, and their proof, are complex and deep. We show that the result continues to hold when utility maximization is replaced by a rationality condition that is even more compelling; more important, the formulation and proof become far more transparent, accessible, and self-contained. |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:huj:dispap:dp652&r=gth |
| By: | Wioletta Dziuda; Ronen Gradwohl |
| Abstract: | Two players choose whether to cooperate on a project. Each of them is endowed with some evidence, and if both possess a sufficient amount then cooperation is profitable. In order to facilitate cooperation the players reveal evidence to one another. However, some players are concerned about privacy, and so revelation of evidence that does not result in cooperation is costly. We show that in equilibrium evidence can be exchanged both incrementally and all at once, and identify conditions under which the different rates of evidence exchange are optimal. |
| Keywords: | Cooperation, Privacy, Communication JEL Classification: D80 |
| Date: | 2013–11–05 |
| URL: | http://d.repec.org/n?u=RePEc:nwu:cmsems:1572&r=gth |
| By: | Ekaterina Sherstyuk (Department of Economics, University of Hawaii at Manoa); Nori Tarui (Department of Economics, University of Hawaii at Manoa); Majah-Leah V. Ravago (School of Economics, University of the Philippines Diliman); Tatsuyoshi Saijo (Kochi University of Technology) |
| Abstract: | Dynamic externalities are at the core of many long-term environmental problems, from species preservation to climate change mitigation. We use laboratory experiments to compare welfare outcomes and underlying behavior in games with dynamic externalities under two distinct settings: traditionally-studied games with infinitely-lived decision makers, and more realistic inter-generational games. We show that if decision makers change across generations, resolving dynamic externalities becomes more challenging for two distinct reasons. First, decision makers’ actions may be short-sighted due to their limited incentives to care about the future generations’ welfare. Second, even when the incentives are perfectly aligned across generations, strategic uncertainty about the follower actions may lead to an increased inconsistency of own actions and beliefs about the others, making own actions more myopic. Inter-generational learning through history and advice from previous generations may improve dynamic efficiency, but may also lead to persistent myopia. |
| Keywords: | economic experiments; dynamic externalities; inter-generational games; climate change |
| JEL: | C92 D62 D90 Q54 |
| Date: | 2013–11 |
| URL: | http://d.repec.org/n?u=RePEc:hai:wpaper:201320&r=gth |
| By: | König, Clemens |
| Abstract: | This paper proposes a novel explanation for the context dependency of individual choices in two-player games. Context dependency refers to the well-established phenomenon that a player, when choosing from a given opportunity set created by the other player’s strategy, chooses differently in different situations because of different alternatives to the other player’s strategy. The utility model used to explain this kind of context dependency incorporates a preference for net-loss reciprocation. Net-loss reciprocation means that a player’s willingness to impose a net loss (i.e., loss minus gain) on the other player increases in the net loss that he or she derives from the other player’s strategy. I show that net-loss reciprocation together with the method for calculating net losses developed in this paper explains the context dependencies in individual behaviour that have been documented in a number of experimental studies, whereas existing models of intention-based reciprocity fail to explain all the evidence. |
| Keywords: | Reciprocity; Fairness; Experimental economics; Game theory; Loss aversion |
| JEL: | C70 C91 D63 D64 |
| Date: | 2013–11–17 |
| URL: | http://d.repec.org/n?u=RePEc:lmu:muenec:17474&r=gth |
| By: | Hammond, Peter J (Department of Economics, University of Warwick); Zank, Horst (University of Manchester) |
| Abstract: | For choice with deterministic consequences, the standard rationality hypothesis is ordinality — i.e., maximization of a weak preference ordering. For choice under risk (resp. uncertainty), preferences are assumed to be represented by the objectively (resp. subjectively) expected value of a von Neumann–Morgenstern utility function. For choice under risk, this implies a key independence axiom; under uncertainty, it implies some version of Savage's sure thing principle. This chapter investigates the extent to which ordinality, independence, and the sure thing principle can be derived from more fundamental axioms concerning behaviour in decision trees. Following Cubitt (1996), these principles include dynamic consistency, separability, and reduction of sequential choice, which can be derived in turn from one consequentialist hypothesis applied to continuation subtrees as well as entire decision trees. Examples of behaviour violating these principles are also reviewed, as are possible explanations of why such violations are often observed in experiments. JEL classification: expected utility ; consequentialism ; independence axiom ; consistent planning ; rationality ; dynamic consistency ; subjective probability ; sure thing principle JEL codes: D01 ; D03 ; D81 ; D91 ; C72 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:1033&r=gth |
| By: | Giampiero Giacomello (Department of Political and Social Studies, University of Bologna, Italy); Luca Lambertini (Department of Economics, University of Bologna, Italy; RCEA, Italy) |
| Abstract: | We model the perspective faced by nuclear powers involved in a supergame where nuclear deterrence is used to stabilise peace. This setting allows us to investigate the bearings of defensive weapons on the effectiveness of deterrence and peace stability, relying on one-shot optimal punishments. We find that the sustainability of peace is unaffected by defensive shields if both countries have them, while asymmetric endowments of such weapons have clearcut destabilising consequences. |
| Keywords: | defensive shields, deterrence, wargames |
| JEL: | C73 F51 |
| Date: | 2013–10 |
| URL: | http://d.repec.org/n?u=RePEc:rim:rimwps:57_13&r=gth |
| By: | Eric Schniter (Economic Science Institute, Chapman University and Argyros School of Business and Economics, Chapman University); Roman M. Sheremeta (Economic Science Institute, Chapman University and Department of Economics, Weatherhead School of Management, Case Western Reserve University); Timothy W. Shields (Economic Science Institute, Chapman University and Argyros School of Business and Economics, Chapman University) |
| Abstract: | We investigated whether 20 emotional states, reported by 170 participants after participating in a Trust game, were experienced in a patterned way predicted by the “Recalibrational Model” or Valence Models. According to the Recalibrational Model, new information about trust-based interaction outcomes triggers specific sets of emotions. Unlike Valence Models that predict reports of large sets of either positive or negative emotional states, the Recalibrational Model predicts the possibility of conflicted (concurrent positive and negative) emotional states. Consistent with the Recalibrational Model, we observed reports of conflicted emotional states activated after interactions where trust was demonstrated but trustworthiness was not. We discuss the implications of having conflicted goals and conflicted emotional states for both scientific and well-being pursuits. |
| Keywords: | emotion, affect valence, recalibrational theory, Trust game, experiment |
| JEL: | C73 C91 D87 |
| Date: | 2013 |
| URL: | http://d.repec.org/n?u=RePEc:chu:wpaper:13-28&r=gth |
| By: | David Goldbaum (Economics Discipline Group, University of Technology, Sydney) |
| Abstract: | This paper introduces a process of individual adjustment based on private local experiences and observation that allows for the emergence of a global social structure that is the equilibrium to the static follow-the-leader game of Goldbaum (2013). The setting rewards agents for being early adopters of popular products or trends. From simple, myopic, self-serving adjustment based on historic evidence by individuals emerges the the equilibrium social structure consisting of a single choice leader and a population of followers, which, in the static setting would require an unlikely degree of coordination to produce. Individual actions take place in a social context with individuals linked via one-way paths of observation. The strategy by which an agent chooses among the available options evolves over time. Different adjustment emergent processes contribute towards the understanding of the unfolding of events that generate the equilibrium structure. |
| Keywords: | Leader; Dynamic Network; Social Interaction; Consumer Choice; Simulation |
| JEL: | D85 D71 C71 |
| Date: | 2013–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:uts:ecowps:15&r=gth |
| By: | Andersson, Ola (Research Institute of Industrial Economics (IFN)); Holm, Håkan J. (Lund University); Tyran, Jean-Robert (University of Vienna); Wengström, Erik (Lund University) |
| Abstract: | We study risk taking on behalf of others in an experiment on a large random sample. The decision makers in our experiment are facing high-powered incentives to increase the risk on behalf of others through hedged compensation contracts or with tournament incentives. Compared to a baseline condition without such incentives, we find that the decision makers respond strongly to these incentives that result in an increased risk exposure of others. However, we find that the increase in risk taking is mitigated by altruistic preferences and pro-social personality traits. |
| Keywords: | Incentives; Competition; Hedging; Risk taking; Social preferences |
| JEL: | C72 C90 D30 D81 |
| Date: | 2013–11–19 |
| URL: | http://d.repec.org/n?u=RePEc:hhs:iuiwop:0989&r=gth |