nep-gth New Economics Papers
on Game Theory
Issue of 2015‒07‒18
24 papers chosen by
László Á. Kóczy
Magyar Tudományos Akadémia

  1. Slow and steady wins the race: approximating Nash equilibria in nonlinear quadratic tracking games By Dimitri Blueschke; Viktoria Blüschke-Nikolaeva; Ivan Savin
  2. The Free Solidarity Value By Bourheneddine Ben Dhaou; Abderrahmane Ziad
  3. Voluntary Provision of a Public Good in a Strategic Market Game By Somdeb LAHIRI
  4. Best response cycles in perfect information games By Herings P.J.J.; Predtetchinski A.
  5. Uniqueness of optimal strategies in captain lotto games By Nadav Amir
  6. Success rates in simplified threshold public goods games: A theoretical model By Feige, Christian
  7. Informational Robustness and Solution Concepts By Dirk Bergemann; Stephen Morris
  8. Mental Representation of Sharing Experimets: Analyzing Choice and Belief Data By Werner Güth; Charlotte Klempt; kerstin Pull
  9. Expectation-Based Loss Aversion and Strategic Interaction By Simon Dato; Andreas Grunewald; Daniel Müller
  10. Can being behind get you ahead? Reference Dependence and Asymmetric Equilibria in an Unfair Tournament By Jan Bergerhoff; Agnes Vosen
  11. On Cobb-Douglas Preferences in Bilateral Oligopoly By Alex DICKINSON
  12. Strategic Interactions and Atoms' Power in Public Goods Economies By Hovav PERETS; Benyamin SHITOVITZ
  13. Threatening Thresholds? The effect of disastrous regime shifts on the cooperative and non-cooperative use of environmental goods and services By Diekert, Florian K.
  14. Evidence Games: Truth and Commitment By Sergiu Hart; Ilan Kremer; Motty Perry
  15. Networked Politics: Political Cycles and Instability under Social Influences By Diffo Lambo, Lawrence; Pongou, Roland; Tchantcho, Bertrand; Wambo, Pierre
  16. Fraudulent Democracy: A Dynamic Ordinal Game Approach By Moyouwou, Issofa; Pongou, Roland; Tchantcho, Bertrand
  17. Distance-based accessibility indices By Csató, László
  18. One Sided Matching: Choice Selection With Rival Uncertain Outcomes By David B. Johnson; Matthew Webb
  19. Deterrence effects under Twombly: on the costs of increasing pleading standards in litigation By Campos, Sergio; Cotton, Christopher; Li, Cheng
  20. On Two-Period Committee Voting: Why Straw Polls Should Have Consequences By Tim Julius Frommeyer
  21. Decentralized Bargaining: Efficiency and the Core By Matt Elliott; Francesco Nava
  22. Failed bank auctions and externalities By Zhou, Tim
  23. Ghost seats in the Basque Parliament By Laruelle, Annick; Ibarzabal Laka, Nora
  24. Partially Binding Platforms: Campaign Promises vis-a-vis Cost of Betrayal By Yasushi Asako

  1. By: Dimitri Blueschke (Alpen-Adria Universität Klagenfurt, Austria); Viktoria Blüschke-Nikolaeva (Alpen-Adria Universität Klagenfurt, Austria); Ivan Savin (Chair of Microeconomics, Friedrich Schiller University Jena, Germany, and Chair for Economic Policy, Karlsruhe Institute of Technology, Germany, and Bureau d'Economie Theorique et Appliquee, France)
    Abstract: We propose a meta-heuristic approach for solving nonlinear dynamic tracking games. In contrast to more 'traditional' methods based on linear-quadratic (LQ) techniques, this derivative-free method is very flexible (e.g. to introduce inequality constraints). The meta-heuristic is applied to a three-player dynamic game and tested versus derivative-dependent method in approximating Nash solution in different game specifications. We demonstrate the superiority of the proposed approach in identifying Nash equilibria, where LQ methods are not applicable.
    Keywords: Dynamic games, Nash equilibrium, Differential Evolution
    JEL: C61 C63 C72 C73 E61
    Date: 2015–07–10
  2. By: Bourheneddine Ben Dhaou (CREM, UMR CNRS 6211, Normandy University, University of Caen Basse-Normandie); Abderrahmane Ziad (CREM, UMR CNRS 6211, Normandy University, University of Caen Basse-Normandie)
    Abstract: In this paper, we consider a cooperative game in which two types of players co-exist: solidary and non solidary players. Solidary players are able to support by consent at least one of their weaker partners without disadvantaging non-solidary players. We present a value of the game which takes ito account the types of players and satisfies some appropriate axioms: Efficiency, Additivity, Symmetry among players who have the same type, Conditional null player, and a new axiom, the Unaffected Allocation of nonsolidary players - (UA) - which is defined as follows: when players have the possibility to decide freely to be solidary, this should affect neither the allocations of non-solidary players, nor the outcome of the game.
    Keywords: Shapley value, Nowak and Radzik value, the free solidarity value, TU cooperative games
    JEL: C71 D60
    Date: 2015–05
  3. By: Somdeb LAHIRI
    Abstract: The purpose of this paper is to investigate the mutual compatibility of the voluntary provision of a public good and the strategic behavior of consumers in the market for private goods. We study the existence of equilibrium in the private provision of a public good within a general strategic equilibrium framework with a finite number of players. The mechanism for the provision of public good follows that of Bergstrom, Blume, and Varian (1986), and the trading mechanism for private goods follows the strategic market game with wash sales of Dubey and Shubik (1986). The paper demonstrates the existence of an equilibrium point in pure strategies for a finite number of players. Due to the existence of trivial equilibria at which all markets are closed, equilibrium points are constructed as limits to sequences of ? - equilibria in perturbed games.
    Keywords: Strategic market game, Public good, Equilibrium points
    JEL: C72 D43 H41
    Date: 2013–12–01
  4. By: Herings P.J.J.; Predtetchinski A. (GSBE)
    Abstract: We consider n-player perfect information games with payoff functions having a finite image. We do not make any further assumptions, so in particular we refrain from making assumptions on the cardinality or the topology of the set of actions and assumptions like continuity or measurability of payoff functions. We show that there exists a best response cycle of length four, that is, a sequence 0, 1, 2, 3, 0 of pure strategy profiles where every successive element is a best response to the previous one. This result implies the existence of point-rationalizable strategy profiles. Whenpayoffs are only required to be bounded, we show the existence of an -best response cycle of length four for every 0.
    Keywords: Noncooperative Games;
    JEL: C72
    Date: 2015
  5. By: Nadav Amir
    Abstract: We consider the class of two-person zero-sum allocation games known as Captain Lotto games (Hart 2014). These are Colonel Blotto type games in which the players have capacity constraints. We show that the players’ optimal strategies are unique in most cases.
    Date: 2015–06
  6. By: Feige, Christian
    Abstract: This paper develops a theoretical model based on theories of equilibrium selection in order to predict success rates in threshold public goods games, i.e., the probability with which a group of players provides enough contribution in sum to exceed a predefined threshold value. For this purpose, a prototypical version of a threshold public goods game is simplified to a 2 x 2 normal-form game. The simplified game consists of only one focal pure strategy for positive contributions aiming at an efficient allocation of the threshold value. The game's second pure strategy, zero contributions, represents a safe choice for players who do not want to risk coordination failure. By calculating the stability sets of these two pure strategies, success rates can be put in explicit relation to the game parameters. It is also argued that this approach has similarities with determining the relative size of the strategies' basins of attraction in a stochastic dynamical system (cf. Kandori, Mailath, and Rob, 1993, Econometrica, Vol. 61, p. 29-56).
    Keywords: threshold public good,coordination games,learning,equilibrium selection
    JEL: C73 H41
    Date: 2015
  7. By: Dirk Bergemann (Cowles Foundation, Yale University); Stephen Morris (Dept. of Economics, Princeton University)
    Abstract: Consider the following "informational robustness" question: what can we say about the set of outcomes that may arise in equilibrium of a Bayesian game if players may observe some additional information? This set of outcomes will correspond to a solution concept that is weaker than equilibrium, with the solution concept depending on what restrictions are imposed on the additional information. We describe a unified approach encompassing prior informational robustness results, as well as identifying the solution concept that corresponds to no restrictions on the additional information; this version of rationalizability depends only on the support of players’ beliefs and implies novel predictions in classic economic environments of coordination and trading games. Our results generalize from complete to incomplete information the classical results in Aumann (1974, 1987) and Brandenburger and Dekel (1987) which can be (and were) given informational robustness interpretations. We discuss the relation between informational robustness and "epistemic" foundations of solution concepts.
    Keywords: Incomplete information, Informational robustness, Bayes correlated equilibrium, Interim corrrelated rationalizability, Belief free rationalizability
    JEL: C72 C79 D82 D83
    Date: 2014–12
  8. By: Werner Güth; Charlotte Klempt; kerstin Pull
    Abstract: We confront allocator participants with dierent sharing games in a within sub- jects design: the Nash demand game, the ultimatum game, the yes-no-game and the impunity game. We allow participants to opt out rather than play the game under consideration. Beside choice data we also collect belief data to learn more about the mental representations of sharing games.
    Date: 2015–03
  9. By: Simon Dato; Andreas Grunewald; Daniel Müller
    Abstract: This paper provides a comprehensive analysis regarding strategic interaction under expectation-based loss-aversion. First, we develop a coherent framework for the analysis by extending the equilibrium concepts of Koszegi and Rabin (2006, 2007) to strategic interaction and demonstrate how to derive equilibria. Second, we delineate how expectation-based loss-averse players differ in their strategic behavior from their counterparts with standard expected-utility preferences. Third, we analyze equilibrium play under expectation-based loss aversion and comment on the existence of equilibria.
    Keywords: Non-Cooperative Games, Expectation-Based Loss Aversion, Reference-Dependent Preferences, Mixed Strategies
    JEL: C72 D01 D03 D81
  10. By: Jan Bergerhoff; Agnes Vosen
    Abstract: Everyone remembers a plot where a disadvantaged individual facing the prospect of failure, spends more effort, turns around the game and wins unexpectedly. Most tournament theories, however, predict the opposite pattern and see the disadvantaged agent investing less effort. We show that ’turn arounds’, i.e. situations where the trailing player spends more effort and becomes the likely winner of the tournament, can be the outcome of a Nash equilibrium when the initial unevenness is known and players have reference-dependent preferences. Under certain conditions, they are the only pure strategy equilibrium. If the initial unevenness is large enough the advantaged player will always invest the most effort. We also show that equilibria in which the player behind catches up without becoming the likely winner do not exist.
    Keywords: loss aversion, gain-loss utility, normal distribution, competition
    JEL: C72 D63 D44
    Date: 2015–02
  11. By: Alex DICKINSON (University of Strathclyde)
    Abstract: Bilateral oligopoly is a simple model of exchange in which a finite set of sellers seek to exchange the goods they are endowed with for money with a finite set of buyers, and no price-taking assumptions are imposed. If trade takes place via a strategic market game bilateral oligopoly can be thought of as two linked proportional-sharing contests: in one the sellers share the aggregate bid from the buyers in proportion to their supply and in the other the buyers share the aggregate supply in proportion to their bids. The analysis can be separated into two ‘partial games’. First, fix the aggregate bid at B; in the first partial game the sellers contest this fixed prize in proportion to their supply and the aggregate supply in the equilibrium of this game is X(B) . Next, fix the aggregate supply at X; in the second partial game the buyers contest this fixed prize in proportion to their bids and the aggregate bid in the equilibrium of this game is . The analysis of these two partial games takes into account competition with ~b (X)in each side of the market. Equilibrium in bilateral oligopoly must take into account competition between sellers and buyers and requires, for example, ~B (~x(b)))=B. When all traders have Cobb-Douglas preference~X(B)s does not depend on B ~B (x) and does not depend on X: whilst there is competition within each side of the market there is no strategic interdependence between the sides of the market. The Cobb-Douglas assumption provides a tractable framework in which to explore the features of fully strategic trade but it misses perhaps the most interesting feature of bilateral oligopoly, the implications of which are investigated
    Keywords: Strategic market game, Bilateral oligopoly, Cobb-Douglas preferences, Aggregative games
    JEL: C72 D43 D50
    Date: 2013–12–01
  12. By: Hovav PERETS (Israel Institute of Technology, Faculty of Industrial Engineering and Management); Benyamin SHITOVITZ (University of Haifa, Department of Economics)
    Abstract: In this paper, we study Nash equilibrium in a smooth public goods economy, described as a noncooperative game, where the set of players is a mixed-measure space of consumers. We assume a finite number of private goods. We show that under certain conditions, there exists a unique Nash equilibrium in the economy, where the public goods are produced with a linear technology. Moreover, we discuss the difference in market power between an atomless sector and an atom with the same utility function and an atom with its split atomless sector in both a pure exchange economy and a public goods economy.
    Keywords: Public Goods, Private provision of public goods, Nash equilibrium, Mixed measure space of consumers, Linear technology
    JEL: C72 H41
    Date: 2013–12–01
  13. By: Diekert, Florian K. (Centre for Ecological and Evolutionary Synthesis, University of Oslo,)
    Abstract: This paper presents an analytically tractable dynamic game in which players jointly use a resource. The resource replenishes fully but collapses should total use exceed a threshold in any one period. The initial level of use is known to be safe. If it is at all optimal to increase resource use, the consumption frontier is pushed once. Moreover, it is shown that the degree of experimentation is decreasing in the safe value of resource use. Non-cooperative agents can take advantage of this feature and coordinate on a “cautious" equilibrium. If the status quo is sufficiently valuable, the threat of the regime shift induces the first-best. If the status-quo is not sufficiently valuable, experimentation will be inefficiently risky. But given that the threshold has not been crossed, the updated consumption frontier will, ex post, be socially optimal. However, there is also a pareto-inferior, “aggressive" equilibrium in which the resource is depleted immediately. Under some conditions, immediate depletion is a self-fulfilling prophecy, although the social optimum is to sustain the resource indefinitely. Closed-form solutions are provided for a specific example and it is shown that the pareto-superior, “cautious" equilibrium is risk-dominant up to a high probability that the opponents play an aggressive strategy. The result that the threat of a disastrous regime shift allows the agents to coordinate on a pareto-superior equilibrium, because it only pays to search for the location of the threshold once, is robust to extensions that account for more general resource dynamics
    Keywords: Dynamic Games; Thresholds and Natural Disasters; Learning
    JEL: C73
    Date: 2015–06–11
  14. By: Sergiu Hart; Ilan Kremer; Motty Perry
    Abstract: An evidence game is a strategic disclosure game in which an agent who has different pieces of verifiable evidence decides which ones to disclose and which ones to conceal, and a principal chooses an action (a "reward"). The agent's preference is the same regardless of his information (his "type")—he always prefers the reward to be as high as possible—whereas the principal prefers the reward to fit the agent's type. We compare the setup where the principal chooses the action only after seeing the disclosed evidence, to the setup where the principal can commit ahead of time to a reward policy (the latter is the standard mechanism-design setup). We compare the setup where the principal chooses the action only after seeing the disclosed evidence to the setup where the principal can commit ahead of time to a reward policy (the mechanism-design setup). The main result is that under natural conditions on the truth structure of the evidence, the two setups yield the same equilibrium outcome.
    Date: 2015–05
  15. By: Diffo Lambo, Lawrence; Pongou, Roland; Tchantcho, Bertrand; Wambo, Pierre
    Abstract: Media, opinion leaders, co-ethnics, family members, and friends influence our political decisions. The ways in which these influences affect political cycles and (in)stability has been understudied. We propose a model of a networked political economy, where agents' choices are partly determined by the opinions of the individuals with whom they are connected in a fixed influence network. The model features two types of individuals: ideological individuals who never change their views and who seek to influence the rest of the society; and non-ideological individuals who have no political allegiance and do not influence anybody, but who can be influenced by ideological individuals with whom they are connected. We show that influence networks increase political turnout and cause non-ideological individuals who are subject to antagonistic influences to keep changing their political views. This in turn increases political cycles and instability in two ways: (1) by reducing the number of stable and popular political leaders; and (2) by worsening the tradeoff between political competition and the existence of a stable leader. We uncover a necessary and sufficient condition that characterizes all of the political technologies and network structures that guarantee political stability. This condition introduces a preference-blind stability index, which maps each pair of a constitution and an influence network into the maximum number of competing political leaders that a society can afford while remaining stable regardless of the extent of preference heterogeneity in its population. Our findings have testable implications for different societies. They shed light on the network origins of political cycles in two-party systems. They also imply that individualist societies are more politically stable than collectivist societies and societies organized around ethnic groups or characterized by a high level of homophilous behavior and influences. For ethnic democracies, we quantify the exact tradeoff between political competition and stability, and show that ethnic fragmentation increases stability. This latter finding further provides a rationale for using the "divide and rule" strategy to maintain political power. Finally, we find that cliques and multi-layer cliques maximize the competition-stability tradeoff, whereas star networks, lines and rings minimize it.
    Keywords: Political cycles, instability, influence networks, homophily, ethnic democracy, competition-stability tradeoff.
    JEL: C0 C7 D7 D8 D85 H0 O1
    Date: 2015–06–01
  16. By: Moyouwou, Issofa; Pongou, Roland; Tchantcho, Bertrand
    Abstract: We propose a model of political competition and stability in nominally democratic societies characterized by fraudulent elections. In each election, an opposition leader is pitted against the leader in power. If the latter wins, he remains in power, which automatically makes him the incumbent candidate in the next election as there are no term limits. If he loses, there is an exogenously positive probability that he will steal the election. We model voter forward-looking behavior, defining a new solution concept. We then examine the existence, popularity, and welfare properties of equilibrium leaders, these being leaders who would remain in power indefinitely without stealing elections. We find that equilibrium leaders always exist. However, they are generally unpopular, and may be inefficient. We identify three types of conditions under which equilibrium leaders are efficient. First, efficiency is achieved under any constitutional arrangement if and only if there are at most four competing leaders. Second, when there are more than four competing leaders, efficiency is achieved if and only if the prevailing political system is an oligarchy, which means that political power rests with a unique minimal coalition. Third, for a very large class of preferences that strictly includes the class of single-peaked preferences, equilibrium leaders are always efficient and popular regardless of the level of political competition. The analysis implies that an excessive number of competing politicians, perhaps due to a high level of ethnic fragmentation, may lead to political failure by favoring the emergence of a ruling leader who is able to persist in power forever without stealing elections, despite being inefficient and unpopular.
    Keywords: Fraudulent democracy, farsightedness, efficiency, popularity, naiveté, political failure, fragmentation
    JEL: C73 D72 D73 K4 O1
    Date: 2015–07–02
  17. By: Csató, László
    Abstract: The paper attempts to develop a suitable accessibility index for networks where each link has a value such that a smaller number is preferred like distance, cost, or travel time. A measure called distance sum is characterized by three independent properties: anonymity, an appropriately chosen independence axiom, and dominance preservation, which requires that a node not far to any other is at least as accessible. We argue for the need of eliminating the independence property in certain applications. Therefore generalized distance sum, a family of accessibility indices, will be suggested. It is linear, considers the accessibility of vertices besides their distances and depends on a parameter in order to control its deviation from distance sum. Generalized distance sum is anonymous and satisfies dominance preservation if its parameter meets a sufficient condition. Two detailed examples demonstrate its ability to reflect the vulnerability of accessibility to link disruptions.
    Keywords: networks, geography, accessibility, distance sum, axiomatic approach
    JEL: D85 Z13
    Date: 2015–06–30
  18. By: David B. Johnson; Matthew Webb (University of Calgary)
    Abstract: We examine decision making in the context of one sided matching: where individuals simultaneously submit several applications to vacancies, each match has an exogenous probability of forming, but each applicant can only fill one vacancy. In these environments individuals choose among interdependent, rival, uncertain outcomes. We design an experiment that has individuals choose a varying number of interdependent lotteries from a fixed set. We find that: 1) with few choices, subjects make safer and riskier choices, 2) subjects behave in a manner inconsistent with expected utility maximizing behavior. We discuss these findings in the context of college application decisions.
    Date: 2015–07–09
  19. By: Campos, Sergio; Cotton, Christopher; Li, Cheng
    Abstract: We develop a stylized game theoretic model of litigant behavior to study the effects of increased pleading standards on incentives to engage in illegal activity. Such a model is necessary to build intuition about the potential costs associated with the procedures set forth by the U.S. Supreme Court in Bell Atlantic Corp. v. Twombly (550 U.S. 544 [2007]) and Ashcroft v. Iqbal (556 U.S. 662, 684 [2009]), which increase the standard of plausibility that lawsuits must meet before being allowed by a judge to proceed to discovery and trial. We show how increasing pleading standards tends to increase illegal activity, and can increase litigation costs. These negative effects should be accounted for when setting a pleading standard. Our results provide a counterpoint to the U.S. Supreme Court’s argument that increased plausibility requirements will decrease the costs of litigation.
    Keywords: Judicial procedure, pleading, litigation, deterrence
    JEL: C72 K41
    Date: 2015–05
  20. By: Tim Julius Frommeyer
    Abstract: We consider a committee voting setup with two rounds of voting where committee members, who possess private information about the state of the world, have to make a binary decision. We investigate incentives for truthful revelation of their information in the first voting period. Coughlan (2000) shows that members reveal their information in a straw poll only if their preferences are in fact homogeneous. By taking costs of time into account, we demonstrate that committees have strictly higher incentives to reveal information if a decision can be made for high levels of consensus in the straw poll already. In such scenarios, members of all homogeneous and some heterogeneous juries are strictly better off when the requirement for early decisions is chosen carefully.
    Keywords: Communication, Committees, Voting
    JEL: D72 D82 D83
    Date: 2015–04
  21. By: Matt Elliott; Francesco Nava
    Abstract: This paper studies market clearing in matching markets. Bargaining in such markets occurs in the context of alternative possible matches that provide endogenous outside options. We ask when will such markets clear efficiently and find inefficiencies, delay and mismatch, to be pervasive. The model is non-cooperative, fully decentralized, and in Markov strategies. Workers and firms bargain with each other to determine who will be matched to whom and on what terms of trade. Once a worker-firm pair reach agreement they exit the market. Delay can extensive and structured with vertically differentiated markets endogenously clearing form the top down. We find mismatch occurs whenever an agent is at risk of loosing a binding endogenous outside option. In both cases inefficiencies are driven by the endogenous evolution of the market.
    Date: 2015–06
  22. By: Zhou, Tim
    Abstract: We measure the negative externalities experienced by non-winning bidders and examine the determinants of these externalities in the Federal Deposit Insurance Corporation (FDIC) failed bank auctions. We show that unsuccessful bidders experience significantly negative cumulative abnormal returns when winning bidders enter non-winning bidders’ key markets as a new entrant by acquiring relatively larger targets and when infrequent bidders are involved.
    Keywords: FDIC, Banks, Auction, Externality
    JEL: D44 D62 G14 G21 G28
    Date: 2015–07–14
  23. By: Laruelle, Annick; Ibarzabal Laka, Nora
    Abstract: In elections voters have generally four options: to abstain, to cast a blank vote, to cast a null vote, or to vote for a candidate or party. This last option is a positive expression of support, while the other three options reflect lack of interest, or dissatisfaction with the parties or the political system. However only votes for parties or candidates are taken into account in the apportionment method. In particular the number of seats allocated to parties remains constant even if the number of non votes (i.e. blank votes, null votes or abstention) is very large. This paper proposes to treat the non votes as a party in the apportionment method and to leave empty the corresponding seats. These empty seats are referred to as "ghost seats". How this would affect the decision-making is quantified in terms of power indices. We apply this proposal to a case study:the regional Parliament of the Basque Autonomous Community (Spain) from 1980 till 2012.
    Keywords: voting, abstention, blanck votes, null votes
    JEL: C71 D72
    Date: 2015–04–24
  24. By: Yasushi Asako (School of Political Science and Economics, Waseda University)
    Abstract: This study examines and models the e?ects of partially binding campaign platforms in a political competition. Here, a candidate who implements a policy that di?ers from the platform must pay a cost of betrayal, which increases with the size of the discrepancy. I also analyze endogenous decisions by citizens to run for an election. In particular, the model is able to show two implications that previous frameworks have had di¢ culty with. First, candidates with di?erent characteristics have di?erent probabilities of winning an election. Second, even knowing that he/she will lose an election, a candidate will still run, hoping to make an opponent?s policy approach his/her own policy.
    Keywords: political competition, endogenous candidates, campaign promises
    JEL: C72 D72
    Date: 2014–08

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