nep-gth New Economics Papers
on Game Theory
Issue of 2019‒04‒29
fifteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Strategic Complements in Two Stage, 2 × 2 Games By Yue Feng; Tarun Sabarwal
  2. Deep Q-Learning for Nash Equilibria: Nash-DQN By Philippe Casgrain; Brian Ning; Sebastian Jaimungal
  3. Observing Actions in Bayesian Games By Dominik Grafenhofer; Wolfgang Kuhle
  4. Financial Transfers and Climate Cooperation By Suzi Kerr; Steffen Lippert; Edmund Lou
  5. Virtual implementation by bounded mechanisms: Complete information By Ritesh Jain; Michele Lombardi
  6. Subjects in the Lab, Activists in the Field: Public Goods and Punishment By Dave, Chetan; Hamre, Sjur; Kephart, Curtis; Reuben, Alicja
  7. Marketing agencies and collusive bidding in online ad auctions By Francesco Decarolis; Maris Goldmanis; Antonio Penta
  8. A General Derivation of Axiomatizations for Allocation Rules: Duality and Anti-Duality Approach By Takayuki Oishi
  9. Penney's Game Odds From No-Arbitrage By Joshua B. Miller
  10. Motivated motive selection in the lying-dictator game By Barron, Kai; Stüber, Robert; van Veldhuizen, Roel
  11. Optimal Destabilization of Cartels By Ludwig von Auer; Tu Anh Pham
  12. Environmental Effects of Capital Income Taxation - A New Double Dividend? By Ritter, Hendrik; Runkel, Marco; Zimmermann, Karl
  13. The large space of information structures By Gensbittel, Fabien; Renault, Jérôme; Peski, Marcin
  14. Information Structures on a General State Space: An Equivalence Theorem and an Application By M. Ali Khan; Haomiao Yu; Zhixiang Zhang
  15. Endogenous Public and Private Leadership with Diverging Social and Private Marginal Costs By Haraguchi, Junichi; Matsumura, Toshihiro

  1. By: Yue Feng (Department of Economics, The University of Kansas); Tarun Sabarwal (Department of Economics, University of Kansas)
    Abstract: Strategic complements are well understood for normal form games, but less so for extensive form games. Indeed, there is some evidence that extensive form games with strategic complemen- tarities are a very restrictive class of games (Echenique (2004)). We explore the extent of this restrictiveness in the context of two stage, 2×2 games. We find that the restrictiveness imposed by quasisupermodularity and single crossing property is particularly severe, in the sense that the set of games in which payoffs satisfy these conditions has measure zero. In contrast, the set of games that exhibit strategic complements (in the sense of increasing best responses) has infinite measure. This enlarges the scope of strategic complements in two stage, 2 × 2 games (and provides a basis for possibly greater scope in more general games). Moreover, the set of subgame perfect Nash equilibria in the larger class of games continues to remain a nonempty, complete lattice.
    Keywords: Strategic complements, extensive form game, two stage game
    JEL: C61 C70
    Date: 2019–03
  2. By: Philippe Casgrain; Brian Ning; Sebastian Jaimungal
    Abstract: Model-free learning for multi-agent stochastic games is an active area of research. Existing reinforcement learning algorithms, however, are often restricted to zero-sum games, and are applicable only in small state-action spaces or other simplified settings. Here, we develop a new data efficient Deep-Q-learning methodology for model-free learning of Nash equilibria for general-sum stochastic games. The algorithm uses a local linear-quadratic expansion of the stochastic game, which leads to analytically solvable optimal actions. The expansion is parametrized by deep neural networks to give it sufficient flexibility to learn the environment without the need to experience all state-action pairs. We study symmetry properties of the algorithm stemming from label-invariant stochastic games and as a proof of concept, apply our algorithm to learning optimal trading strategies in competitive electronic markets.
    Date: 2019–04
  3. By: Dominik Grafenhofer; Wolfgang Kuhle
    Abstract: We study Bayesian coordination games where agents receive noisy private information over the game's payoff structure, and over each others' actions. If private information over actions is precise, we find that agents can coordinate on multiple equilibria. If private information over actions is of low quality, equilibrium uniqueness obtains like in a standard global games setting. The current model, with its flexible information structure, can thus be used to study phenomena such as bank-runs, currency crises, recessions, riots, and revolutions, where agents rely on information over each others' actions.
    Date: 2019–04
  4. By: Suzi Kerr (Motu Economic and Public Policy Research); Steffen Lippert (University of Auckland); Edmund Lou (Motu Economic and Public Policy Research)
    Abstract: We investigate the impact of side-payments to countries that have a low net benefit from participating in efficient climate cooperation in a repeated games framework with investment in different technologies. We consider different timings of these payments and different degrees of commitment. If countries cannot commit ex ante to transfer funds to low-benefit participants to an agreement, then there is a trade-off. Investment based agreements, where transfers occur before emissions are realized, but after investments have been committed, maximize the scope of cooperation. Results-based agreements minimize transfers whenever these agreements implement cooperation. If countries can commit to transfer funds, then agreements in which countries with high benefits of climate cooperation pre-commit to results-based payments to countries with low benefits both maximize the scope of cooperation and minimize transfers.
    Keywords: Game theory, cooperation, repeated games, climate change, international agreement
    JEL: Q54 Q56 Q58 F55 F53
    Date: 2019–03
  5. By: Ritesh Jain (Institute of Economics, Academia Sinica, Taipei, Taiwan); Michele Lombardi (Adam Smith Business School, University of Glasgow.)
    Abstract: A social choice rule (SCR) F maps preference profiles to lotteries over some finite set of outcomes. F is virtually implementable in (pure and mixed) Nash equilibria provided that for all E > 0, there exists a mechanism such that for each preference profile t, its set of Nash equilibrium outcomes at t is E-closed to the socially desirable set F(t). Under a domain restriction, we obtain the following result: When there are at least three agents, any F is virtually implementable in Nash equilibrium, as well as in rationalizable strategies, by a bounded mechanism. No "tail-chasing" constructions, common in the constructive proofs of the literature, is used to assure that undesired strategy combinations do not form a Nash equilibrium.
    Keywords: : Virtual implementation, pure and mixed Nash equilibria, rationalizability, social choice rules
    JEL: C79 D82
    Date: 2019–04
  6. By: Dave, Chetan (University of Alberta, Department of Economics); Hamre, Sjur (Duke University); Kephart, Curtis (R-Studio); Reuben, Alicja (New York University Abu Dhabi)
    Abstract: We compare standard (laboratory) and non-standard (field) subject pool behavior in an extensive form public goods game with random punishment. Our experimental investigation is motivated by real-world ‘Activists’ encouraging public goods provision by firms; an activity known as corporate social responsibility. We find that relative to laboratory subjects, activists in Mumbai are more willing to settle at the Nash equilibrium of the game (which entails increased provision of public goods) and are more willing to punish non-cooperative firm behavior even if such punishments hurt their own payoffs.
    Keywords: Public goods; punishment; non-standard subject pool
    JEL: C92 C93 D64
    Date: 2019–04–23
  7. By: Francesco Decarolis; Maris Goldmanis; Antonio Penta
    Abstract: The transition of the advertising market from traditional media to the internet has induced a proliferation of marketing agencies specialized in bidding in the auctions that are used to sell ad space on the web. We analyze how collusive bidding can emerge from bid delegation to a common marketing agency and how this can undermine the revenues and allocative efficiency of both the Generalized Second Price auction (GSP, used by Google and Microsoft-Bing and Yahoo!) and the of VCG mechanism (used by Facebook). We find that, despite its well-known susceptibility to collusion, the VCG mechanism outperforms the GSP auction both in terms of revenues and efficiency.
    Keywords: Collusion, digital marketing agencies, facebook, google, GSP, internet auctions, online advertising, VCG
    JEL: C72 D44 L81
    Date: 2019–04
  8. By: Takayuki Oishi (Faculty of Economics, Meisei University)
    Abstract: We offer a general derivation of axiomatizations for allocation rules, referred to as "duality" and "anti-duality" approach. We show basic properties of duality and antiduality approach. Using these properties, we can derive axiomatizations of allocation rules by taking (anti-)dual of axioms involved in axiomatizations of their self-(anti-)dual rules. As an illustration, we derive a new axiomatization of the Shapley value for bidding ring problems from using the notion of duality and axioms involved in axiomatizations of the Shapley value for airport problems. As another illustration, we derive a new axiomatization of the nucleolus for bidding ring problems from using the notion of antiduality and axioms involved in axiomatizations of the nucleolus for airport problems.
    Keywords: duality, anti-duality, axiomatization, Shapley value, nucleolus
    JEL: C69 C71
    Date: 2019–03–28
  9. By: Joshua B. Miller
    Abstract: Penney's game is a two player zero-sum game in which each player chooses a three-flip pattern of heads and tails and the winner is the player whose pattern occurs first in repeated tosses of a fair coin. Because the players choose sequentially, the second mover has the advantage. In fact, for any three-flip pattern, there is another three-flip pattern that is strictly more likely to occur first. This paper provides a novel no-arbitrage argument that generates the winning odds corresponding to any pair of distinct patterns. The resulting odds formula is equivalent to that generated by Conway's "leading number" algorithm. The accompanying betting odds intuition adds insight into why Conway's algorithm works. The proof is simple and easy to generalize to games involving more than two outcomes, unequal probabilities, and competing patterns of various length. Additional results on the expected duration of Penney's game are presented. Code implementing and cross-validating the algorithms is included.
    Date: 2019–03
  10. By: Barron, Kai; Stüber, Robert; van Veldhuizen, Roel
    Abstract: A large body of evidence suggests that people are willing to sacrifice personal material gain in order to adhere to a moral motive such as fairness or truth-telling. Yet less is known about what happens when moral motives are in conflict. We hypothesize that in such situations, individuals engage in what we term ‘motivated motive selection’, choosing to adhere to the motive that most closely aligns with their personal interest. We test this hypothesis using a laboratory experiment that induces in subjects a conflict between two of the most-studied moral motives: fairness and truth-telling. Our experimental design has the attractive features of being both parsimonious and closely related to both the classic dictator and lying games, implying comparability with a wealth of benchmark evidence. In line with our hypothesis, our results suggest that participants are more likely to adhere to the motive that is more in line with their self-interest.
    Keywords: Motivated reasoning,dictator game,lying game,motives,moral dilemma
    JEL: C91 D01 D63 D90
    Date: 2019
  11. By: Ludwig von Auer; Tu Anh Pham
    Abstract: The literature on cartel stability sidelines antitrust policy, whereas the literature on antitrust policy tends to neglect issues of cartel stability. This paper attempts to connect these two interrelated aspects in the context of an augmented quantity leadership model. The cartel is the Stackelberg quantity leader and the fringe firms are in Cournot competition with respect to the residual demand. The antitrust authority decides on its own investigative effort and on the size of the fine that cartel members have to pay when they are detected. For testifying cartel members a leniency program is implemented. Our framework takes into account that these antitrust policy instruments are not costless for society. Our model demonstrates that the optimal antitrust policy exploits the inherent instability of a cartel to reduce its size.
    Keywords: antitrust, stability, Cournot fringe, oligopoly, leniency
    JEL: L13 L41
    Date: 2019
  12. By: Ritter, Hendrik; Runkel, Marco; Zimmermann, Karl
    Abstract: We analyze a n-country, two-period Nash tax competition game to evaluate Sinn’s proposal to use capital income taxation as a means to decelerate fossil fuel ex- traction (Sinn, 2008). The interest and discount rate is determined on a perfectly competitive consumer loan market on which the resource extractor acts as the loan supplier. Our first result is that, with perfectly identical countries, tax rates are inefficiently low in the Nash equilibrium of the tax competition game since the tax distortion and the environmental externality are not taken into account. The sec- ond result is that, in an asymmetric setting with resource-exporting and -importing countries, the tax can turn into a subsidy in the exporting country. Moreover, we show that partial cooperation of the importers is always beneficial to them, but can be harmful to the exporter. Finally, we identify cases where full cooperation is self-enforcing.
    Keywords: Capital taxation,Green paradox,Non-renewable resources
    JEL: H21 H23 Q38 Q54
    Date: 2019
  13. By: Gensbittel, Fabien; Renault, Jérôme; Peski, Marcin
    JEL: C70
    Date: 2019–04
  14. By: M. Ali Khan (Department of Economics, Johns Hopkins University, USA); Haomiao Yu (Department of Economics, Ryerson University, Canada); Zhixiang Zhang (CEMA, Central University of Finance and Economics, China)
    Abstract: Blackwell's (1949) theorem on the comparison of information structures has been influential in both theoretical and applied work in economics, statistics and game theory, but severely hampered by its confinement to finite state spaces. Applications and alternative proofs have all suffered from this limitation, though in their use of continuous density functions, not all authors have realized this. In this note, we remove this dissonance that has dogged the literature at least since Boll's (1955) announcement. We do so by working with an abstract, measurable state-space and a Polish observation space, and as one application, apply the theorem to generalize the Hirshleifer-Schlee result on the value of information in a Walrasian price-taking environment. We relate our results to a broad selection of the antecedent (inter-disciplinary) literature.
    Keywords: Information structure, sufficiency, informativeness, second-order stochastic dominance, mean-preserving spread, martingalizability, Hirshleifer effect
    JEL: C6 D5 D8
    Date: 2019–04
  15. By: Haraguchi, Junichi; Matsumura, Toshihiro
    Abstract: We investigate endogenous timing in a mixed duopoly with price competition and with social marginal cost differing from private marginal costs. We find that any equilibrium timing patterns--Bertrand, Stackelberg with private leadership, Stackelberg with public leadership, and multiple Stackelberg equilibria-- emerge. When the foreign ownership share in a private firm is less than 50%, public leadership more likely emerges than private leadership. Conversely, private leadership can emerge in a unique equilibrium when the foreign ownership share in a private firm is large. These results may explain recent policy changes in public financial institutions in Japan. We also find a nonmonotone relationship between the welfare advantage of public and private leadership and the difference between social and private marginal costs for a private firm. A nonmonotone relationship does not emerge in profit ranking.
    Keywords: public financial institutions, differentiated products, Bertrand, Stackelberg, payoff dominance
    JEL: H42 L13
    Date: 2019–04–20

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