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  1. Disequilibrium play in tennis
    Autor*in: Anderson, Axel; Rosen, Jeremy; Rust, John; Wong, Kin-Ping
    Erschienen: [2023]
    Verlag:  SSRN, [S.l.] ; Georgetown University, Department of Economics, Washington, DC

    Are the serves of the world’s best tennis pros consistent with the theoretical predictions of Nash equilibrium in mixed strategies? We analyze their serve direction choices (to the receiver’s left, right or body) with data from an online database... mehr

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    Are the serves of the world’s best tennis pros consistent with the theoretical predictions of Nash equilibrium in mixed strategies? We analyze their serve direction choices (to the receiver’s left, right or body) with data from an online database called the Match Charting Project. Using a new methodology, we test and decisively reject a key implication of a mixed strategy Nash equilibrium, namely, that the probability of winning a service game is the same for all serve directions. We also use dynamic programming (DP) to numerically solve for the best-response serve strategies in models of the service game of tennis estimated for individual server-receiver pairs, such as Novak Djokovic serving to Rafael Nadal. We show that for most elite professional servers, the DP serve strategy significantly increases their service game win probability compared to the mixed strategies they actually use, which we estimate using flexible reduced-form logit models. Stochastic simulations verify that our results are robust to estimation error

     
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    Sprache: Englisch
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    Schriftenreihe: Working papers / Georgetown University, Department of Economics ; 23-23-03
    Schlagworte: tennis; games; Nash equilibrium; Minimax theorem; constant sum games; mixed strategies; dynamic directional games; binary Markov games; dynamic programming; structural estimation; muscle memory; magnification effect
    Umfang: 1 Online-Ressource (circa 84 Seiten)
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    Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments March 9, 2023 erstellt
  2. Linear-quadratic-singular stochastic differential games and applications
    Autor*in: Dianetti, Jodi
    Erschienen: [2023]
    Verlag:  Center for Mathematical Economics (IMW), Bielefeld University, Bielefeld, Germany

    We consider a class of non-cooperative N-player non-zero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is quadratic in... mehr

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    We consider a class of non-cooperative N-player non-zero-sum stochastic differential games with singular controls, in which each player can affect a linear stochastic differential equation in order to minimize a cost functional which is quadratic in the state and linear in the control. We call these games linear-quadratic-singular stochastic differential games. Under natural assumptions, we show the existence of open-loop Nash equilibria, which are characterized through a linear system of forward-backward stochastic differential equations. The proof is based on an approximation via a sequence of games in which players are restricted to play Lipschitz continuous strategies. We then discuss an application of these results to a model of capacity expansion in oligopoly markets.

     
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    hdl: 10419/278468
    Schriftenreihe: Working papers / Center for Mathematical Economics ; 678 (April 2023)
    Schlagworte: Singular stochastic control; linear quadratic games; stochastic maximum principle; Nash equilibrium
    Umfang: 1 Online-Ressource (circa 22 Seiten)
  3. A game-theoretic implication of the Riemann Hypothesis
    Autor*in: Ewerhart, Christian
    Erschienen: [2023]
    Verlag:  University of Zurich, Department of Economics, Zurich

    The Riemann Hypothesis (RH) is one of the major unsolved problems in pure mathematics. In this note, a parameterized family of non-cooperative games is constructed with the property that, if RH holds true, then any game in this family admits a unique... mehr

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    The Riemann Hypothesis (RH) is one of the major unsolved problems in pure mathematics. In this note, a parameterized family of non-cooperative games is constructed with the property that, if RH holds true, then any game in this family admits a unique Nash equilibrium. We argue that this result is not degenerate. Indeed, neither is the conclusion a tautology, nor is RH used to define the family of games.

     
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    hdl: 10419/275654
    Auflage/Ausgabe: Revised version, May 2023
    Schriftenreihe: Working paper series / University of Zurich, Department of Economics ; no. 410
    Schlagworte: Riemann hypothesis; Nash equilibrium
    Umfang: 1 Online-Ressource (circa 25 Seiten), Illustrationen
  4. The n-player Hirshleifer contest
    Autor*in: Ewerhart, Christian; Sun, Guang-Zhen
    Erschienen: [2023]
    Verlag:  University of Zurich, Department of Economics, Zurich

    While the game-theoretic analysis of conflict is often based on the assumption of multiplicative noise, additive noise such as considered by Hirshleifer (1989) may be equally plausible depending on the application. In this paper, we examine the... mehr

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    While the game-theoretic analysis of conflict is often based on the assumption of multiplicative noise, additive noise such as considered by Hirshleifer (1989) may be equally plausible depending on the application. In this paper, we examine the equilibrium set of the n-player difference-form contest with heterogeneous valuations. For high and intermediate levels of noise, the equilibrium is in pure strategies, with at most one player being active. For small levels of noise, however, we find a variety of equilibria in which some but not necessarily all players randomize. In the case of homogeneous valuations, we obtain a partial uniqueness result for symmetric equilibria. As the contest becomes increasingly decisive, at least two contestants bid up to the valuation of the second-ranked contestant, while any others ultimately drop out. Thus, in the limit, equilibria of the Hirshleifer contest share important properties of equilibria of the corresponding all-pay auction.

     
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    hdl: 10419/278787
    Auflage/Ausgabe: Revised version, October 2023
    Schriftenreihe: Working paper series / University of Zurich, Department of Economics ; no. 361
    Schlagworte: Difference-form contests; Nash equilibrium; rent dissipation; all-pay auction
    Umfang: 1 Online-Ressource (circa 43 Seiten), Illustrationen
  5. On the solution of games with arbitrary payoffs
    an application to an over-the- counter financial market
    Autor*in: Kollias, Iraklis; Leventides, John; Papavassiliou, Vassilios G.
    Erschienen: [2023]
    Verlag:  Geary Institute, University College Dublin, [Dublin]

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    Schriftenreihe: UCD Geary Institute for Public Policy discussion paper series ; Geary WP2023, 02 (January 05, 2023)
    Schlagworte: Game theory; Soft set theory; Nash equilibrium; Cooperative bargaining games; Over-the-counter financial markets; Financial intermediation
    Umfang: 1 Online-Ressource (circa 43 Seiten)
  6. The punctuality stability of the Nash equilibrium: the advantage of a late player in potential and aggregative games
    Autor*in: Gusev, Vasily V.
    Erschienen: 2023
    Verlag:  National Research University, Higher School of Economic, [Moscow]

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    Schriftenreihe: Array ; 261/EC/2023
    Schlagworte: Nash equilibrium; punctuality stability; potential games; aggregative games; symmetricgames
    Umfang: 1 Online-Ressource (circa 32 Seiten), Illustrationen