nep-gth New Economics Papers
on Game Theory
Issue of 2017‒01‒15
seventeen papers chosen by
László Á. Kóczy
Magyar Tudományos Akadémia

  1. Pareto dominance of deferred acceptance through early decision By BONKOUNGOU, Somouaoga
  2. Strategy proofness and unanimity in many-to-one matching markets By Diss, Mostapha; Doghmi, Ahmed; Tlidi, Abdelmonaim
  3. The Shapley Value of Digraph Games By Krishna Khatri
  4. Zero-Sum Revision Games By Gensbittel, Fabien; Lovo, Stefano; Renault, Jérôme; Tomala, Tristan
  5. Hidden Stochastic Games and Limit Equilibrium Payoffs By Renault, Jérôme; Ziliotto, Bruno
  6. All-Pay Auctions with Ties By Alan Gelder; Dan Kovenock; Brian Roberson
  7. Assigning refugees to landlords in Sweden: stable maximum matchings By ANDERSSON, Tommy; EHLERS, Lars
  8. Nash equilibrium with discontinuous utility functions: Reny's approach extended By Kukushkin, Nikolai S.
  9. Equilibria in a Japanese-English Auction with Discrete Bid Levels for the Wallet Game By Ray, Indrajit; Gonçalves, Ricardo
  10. Games with the Total Bandwagon Property By Honda, Jun
  11. An Axiomatization of the Proportional Rule in Financial Networks By Csoka, Péter; Herings, P. Jean-Jacques
  12. A game model of new and remanufactured goods, brown and green consumers, and market share dominance By Amit Batabyal; Hamid Beladi
  13. Asymmetric Power and Market Failure: Power Hazard in Exchange By Korkut Erturk
  14. Credit Where Credit Is Due: An Approach to Education Returns Based on Shapley Values By Barakat, Bilal; Crespo Cuaresma, Jesus
  15. Learning to trust, learning to be trustworthy By Berger, Ulrich
  16. A distance for probability spaces, and long-term values in Markov Decision Processes and Repeated Games By Renault, Jérôme; Venel, Xavier
  17. Three Essays on the Theory of Money and Financial Institutions Essay 3: The Economy with Innovation, Externalities and Context By Martin Shubik

  1. By: BONKOUNGOU, Somouaoga
    Abstract: An early decision market is governed by rules that allow each student to apply to (at most) one college and require the student to attend this college if admitted. This market is ubiquitous in college admissions in the United States. We model this market as an extensive-form game of perfect information and study a refinement of subgame perfect equilibrium (SPE) that induces undominated Nash equilibria in every subgame (SPUE). Our main result shows that this game can be used to define a decentralized matching mechanism that weakly Pareto dominates student-proposing deferred acceptance.
    Keywords: Early decision; Pareto dominance; decentralized market; subgame perfect; equilibrium; subgame perfect undominated Nash equilibrium; costly application
    JEL: C78 C72 C73 I29
    Date: 2016
  2. By: Diss, Mostapha; Doghmi, Ahmed; Tlidi, Abdelmonaim
    Abstract: In this paper, we consider a standard model of many-to-one matching markets. First, we study the relation between strategy-proofness and unanimity under a certain requirement and we prove these two properties become equivalent. Second, we illustrate that this result has an immediate impact on the relation between strategy-proofness and Maskin monotonicity. Finally, we determine a close connexion between strategy-proofness and implementation literature. We provide under certain minimal requirements the foundation for reasoning the equivalence among dominant strategy implementation, standard Nash implementation, and partially honest Nash implementation.
    Keywords: Many-to-one matching markets; strategy-proofness; unanimity; Maskin monotonicity, implementation.
    JEL: C72 C78 D71
    Date: 2016–12–08
  3. By: Krishna Khatri
    Abstract: In this paper the Shapley value of digraph (directed graph) games are considered. Digraph games are transferable utility (TU) games with limited cooperation among players, where players are represented by nodes. A restrictive relation between two adjacent players is established by a directed line segment. Directed line segments, connecting the initial player with the terminal player, form the coalition among players. Dominance relation is established between players and this relation determines whether or not a player wants to cooperate. To cooperate, we assume player joins coalition where he/she is not dominated by any other players. The Shapley value is defines as the average of marginal contribution vectors corresponding to all permutations that do not violate the subordination of players. The Shapley value for various digraph games is calculated and analyzed. For a given characteristic function, a quick way to calculated Shapley values is formulated.
    Date: 2017–01
  4. By: Gensbittel, Fabien; Lovo, Stefano; Renault, Jérôme; Tomala, Tristan
    Abstract: In a zero-sum asynchronous revision game, players can revise their actions only at exogenous random times. Players’ revision times follow Poisson processes, independent across players. Payoffs are obtained only at the deadline by implementing the last prepared actions in the ‘component game’. The value of this game is called revision value. We characterize it as the unique solution of an ordinary differential equation and show it is continuous in all parameters of the model. We show that, as the duration of the game increases, the limit revision value does not depend on the initial position and is included between the min-max and max-min of the component game. We fully characterize the equilibrium in 2?2 games. When the component game minmax and maxmin differ, the revision game equilibrium paths have a wait-and-wrestle structure: far form the deadline, players stay put at sur-place action profile, close to the deadline, they take best responses to the action of the opponent.
    Keywords: Revision Games, Zero-sum Games, Deadline Effect.
    Date: 2017–01
  5. By: Renault, Jérôme; Ziliotto, Bruno
    Abstract: We consider 2-player stochastic games with perfectly observed actions, and study the limit, as the discount factor goes to one, of the equilibrium payoffs set. In the usual setup where current states are observed by the players, we first show that the set of stationary equilibrium payoffs always converges. We then provide the first examples where the whole set of equilibrium payoffs diverges. The construction can be robust to perturbations of the payoffs, and to the introduction of normal-form correlation. Next we naturally introduce the more general model of hidden stochastic game, where the players publicly receive imperfect signals over current states. In this setup we present a last example where not only the limit set of equilibrium payoffs does not exist, but there is no converging selection of equilibrium payoffs. The example is symmetric and robust in many aspects, in particular to the introduction of extensive-form correlation or communication devices. No uniform equilibrium payoff exists, and the equilibrium set has full support for each discount factor and each initial state.
    Date: 2017–01
  6. By: Alan Gelder (Institute for Defense Analyses); Dan Kovenock (Economic Science Institute, Chapman University); Brian Roberson (Department of Economics, Purdue University)
    Abstract: We study the two-player, complete information all-pay auction in which a tie ensues if neither player outbids the other by more than a given amount. In the event of a tie, each player receives an identical fraction of the winning prize. Thus players engage in two margins of competition: losing versus tying, and tying versus winning. Two pertinent parameters are the margin required for victory and the value of tying relative to winning. We fully characterize the set of Nash equilibria for the entire parameter space. For much of the parameter space, there is a unique Nash equilibrium which is also symmetric. Equilibria typically involve randomizing over multiple disjoint intervals, so that in essence players randomize between attempting to tie and attempting to win. In equilibrium, expected bids and payoffs are non-monotonic in both the margin required for victory and the relative value of tying.
    Keywords: All-pay auction, contest, tie, draws, bid differential
    JEL: C72 D44 D72 D74
    Date: 2016
  7. By: ANDERSSON, Tommy; EHLERS, Lars
    Abstract: The member states of the European Union received 1.2 million first time asylum applications in 2015 (a doubling compared to 2014). Even if asylum will be granted for many of the refugees that made the journey to Europe, several obstacles for successful integration remain. This paper focuses on one of these obstacles, namely the problem of finding housing for refugees once they have been granted asylum. In particular, the focus is restricted to the situation in Sweden during 2015–2016 and it is demonstrated that market design can play an important role in a partial solution to the problem. More specifically, because almost all accommodation options are exhausted in Sweden, the paper investigates a matching system, closely related to the system adopted by the European NGO “Refugees Welcome”, and proposes an easy-to-implement algorithm that finds a stable maximum matching. Such matching guarantees that housing is provided to a maximum number of refugees and that no refugee prefers some landlord to their current match when, at the same time, that specific landlord prefers that refugee to his current match.
    Keywords: Refugees; private landlords; forced migration; market design; stable maximum matchings
    JEL: C71 C78 D71 D78 F22
    Date: 2016
  8. By: Kukushkin, Nikolai S.
    Abstract: Philip Reny's approach to games with discontinuous utility functions can work outside its original context. The existence of Nash equilibrium, as well as the possibility to approach an equilibrium with a finite individual improvement path, are established, under a condition slightly weaker than the better reply security, for three classes of strategic games: potential games, games with strategic complementarities, and aggregative games with appropriate monotonicity conditions.
    Keywords: better reply security; Nash equilibrium; potential game; game with strategic complementarities; aggregative game
    JEL: C72
    Date: 2016–12–28
  9. By: Ray, Indrajit (Cardiff Business School); Gonçalves, Ricardo (Católica Porto Business School)
    Abstract: We consider the set-up of a Japanese-English auction with exogenously fixed discrete bid levels for the wallet game with two bidders. We prove that bidding twice the signal - the equilibrium strategy with continuous bid levels - is never an equilibrium in this set up. We show that partition equilibria exist that may be separating or pooling. We illustrate some separating and pooling equilibria with two and three discrete bid levels; we also compare the revenues of the seller from these equilibria and thereby find the optimal bid levels in these cases.
    Keywords: Japanese-English auctions, wallet game, discrete bids, partitions, pooling equilibrium, separating equilibrium
    JEL: C72 D44
    Date: 2016
  10. By: Honda, Jun
    Abstract: We consider the class of two-player symmetric n x n games with the total bandwagon property (TBP) introduced by Kandori and Rob (1998). We show that a game has TBP if and only if the game has 2^n - 1 symmetric Nash equilibria. We extend this result to bimatrix games by introducing the generalized TBP. This sheds light on the (wrong) conjecture of Quint and Shubik (1997) that any n x n bimatrix game has at most 2^n - 1 Nash equilibria. As for an equilibrium selection criterion, I show the existence of a ½-dominant equilibrium for two subclasses of games with TBP: (i) supermodular games; (ii) potential games. As an application, we consider the minimum-effort game, which does not satisfy TBP, but is a limit case of TBP. (author's abstract)
    Keywords: Bandwagon; Nash Equilibrium; Number of Equilibria; Coordination Game; Equilibrium Selection
    Date: 2015–07
  11. By: Csoka, Péter (corvinus university of budapest); Herings, P. Jean-Jacques (General Economics 1 (Micro))
    Abstract: The most important rule to determine payments in real-life bankruptcy problems is the proportional rule. Many bankruptcy problems are characterized by network aspects and default may occur as a result of contagion. Indeed, in financial networks with defaulting agents, the values of the agents' assets are endogenous as they depend on the extent to which claims on other agents can be collected. These network aspects make an axiomatic analysis challenging. This paper is the first to provide an axiomatization of the proportional rule in financial networks. Our two central axioms are impartiality and non-manipulability by identical agents. The other axioms are claims boundedness, limited liability, priority of creditors, and continuity.
    Keywords: financial networks, systemic risk, bankruptcy rules, proportional rule
    JEL: C71 G10
    Date: 2017
  12. By: Amit Batabyal; Hamid Beladi
    Abstract: The n total consumers in the market for a particular good are made up of b brown and g green consumers so that b+g=n. The b brown (g green) consumers are not (are) environmentally conscious and hence they prefer to buy a new (remanufactured) good denoted by N and R respectively. By strategically purchasing or not purchasing the N and the R goods, the brown and the green consumers attempt to create a dominant market share for their preferred good. In this setting, we study three issues. First, we delineate the game between the brown and the green consumers in normal form and then solve for the Nash equilibrium when n=2 and b=1. Second, we find all the Nash equilibria of this game between brown and green consumers when n>2 is an even number and b=g=n/2. Finally, we increase the cost of purchasing the new and the remanufactured goods and then study how this increase affects the answers obtained for the above two issues.
    Keywords: Brown Consumer; Green Consumer; Market Share; New Good; Remanufactured Good
    JEL: D11 Q20
    Date: 2016–12
  13. By: Korkut Erturk
    Abstract: In simple textbook treatment of bilateral exchange traders end up on the contract curve such that the trading surplus is maximized regardless of any asymmetric bargaining power they might have. However, that need not be true when the terms of exchange are determined by uncooperative bargaining, for gains from trading will not reach its potential unless traders refrain from acting strategically. But, because power asymmetry creates quasi-rents that the more powerful player can capture, she might maximize her payoff when total gain from trading falls short of its potential. In other words, power asymmetry can make acting strategically tempting for the more powerful player, which however is socially costly. Using game theory the paper specifies profit maximizing strategic behavior under asymmetric power and considers its relevance for a more general conception of market exchange where traders bargain strategically. Two examples, involuntary unemployment and North’s theory of the state, are then discussed in light of the model developed.
    Keywords: Asymmetric Power, Rent Seeking, Uncooperative Games, Strategic Bargaining JEL Classification: A10, D70, C70, E02
    Date: 2016
  14. By: Barakat, Bilal; Crespo Cuaresma, Jesus
    Abstract: We propose the use of methods based on the Shapley value to assess the fact that private returns to lower levels of educational attainment should incorporate prospective returns from higher attainment levels, since achieving primary education is a necessary condition to enter secondary and tertiary educational levels. We apply the proposed adjustment to a global dataset of private returns to different educational attainment levels and find that the corrected returns to education imply a large shift of returns from tertiary to primary schooling in countries at all income levels. (authors' abstract)
    Keywords: Returns to education; Shapley value
    Date: 2016–06
  15. By: Berger, Ulrich
    Abstract: Interpersonal trust is a one-sided social dilemma. Building on the binary trust game, we ask how trust and trustworthiness can evolve in a population where partners are matched randomly and agents sometimes act as trustors and sometimes as trustees. Trustors have the option to costly check a trustee's last action and to condition their behavior on the signal they receive. We show that the resulting population game admits two components of Nash equilibria. Nevertheless, the long-run outcome of an evolutionary social learning process modeled by the best response dynamics is unique. Even if unconditional distrust initially abounds, the trustors' checking option leads trustees to build a reputation for trustworthiness by honoring trust. This invites free-riders among the trustors who save the costs of checking and trust blindly, until it does no longer pay for trustees to behave in a trustworthy manner. This results in cyclical convergence to a mixed equilibrium with behavioral heterogeneity where suspicious checking and blind trusting coexist while unconditional distrust vanishes. (author's abstract)
    Keywords: trust game; evolutionary game theory; reputation; best response dynamics
    Date: 2016–01
  16. By: Renault, Jérôme; Venel, Xavier
    Keywords: Markov decision processes, gambling houses, POMDPs, repeated games, distance for belief spaces, Kantorovich-Rubinstein duality, Wasserstein metric, limit value, uniform value, general values, characterization of the value.
    Date: 2017–01
  17. By: Martin Shubik (Cowles Foundation, Yale University)
    Abstract: This essay is the third of three. The first is nontechnical and in part autobiograhpical describing the evolution of my approach to developing a microeconomic theory of money institutions. The second essay was devoted to a more formal sketch of a closed economic exchange system with no other externalities beyond money and markets. This essay builds on the existence of monetary exchange but also context, and active government with nonsymmetric information and many externaties indicate that the views of Keynes, Hayek and Schumpeter are all consistent with the next stages of complexity as the logic requires many different arrays of institutions to provide the necessary economic functions and adjust to the variety of socio-economic contexts.
    Keywords: Schumpeter, Keynes, aggregation, information, disequilibrium, minimal institutions, innovation, playable games
    JEL: C7 D50 E4
    Date: 2016–12

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