nep-gth New Economics Papers
on Game Theory
Issue of 2021‒02‒22
eighteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Beliefs in Repeated Games By Masaki Aoyagi; Guillaume Frechette; Sevgi Yuksel
  2. Competing Mechanisms and Folk Theorems: Two Examples By Andrea Attar; Eloisa Campioni; Thomas Mariotti; Gwenaël Piaser
  3. Strategic justifications of the TAL-family of rules for bankruptcy problems By Juan D. Moreno-Ternero; Min-Hung Tsay; Chun-Hsien Yeh
  4. Full Collusion with Entry and Incomplete Information By Ramakanta Patra; Tadashi Sekiguchi
  5. Myopic reallocation of extraction improves collective outcomes in networked common-pool resource games By Schauf, Andrew; Oh, Poong
  6. Private and common value auctions with ambiguity over correlation By Laohakunakorn, Krittanai; Levy, Gilat; Razin, Ronny
  7. Liberalism, rationality, and Pareto optimality By Shaun Hargreaves Heap; Mehmet S. Ismail
  8. The core for housing markets with limited externalities By Bettina Klaus
  9. Strategic Uncertainty and Probabilistic Sophistication By Masaki Aoyagi; Takehito Masuda; Naoko Nishimura
  10. A Balance for Fairness: Fair Distribution Utilising Physics in Games of Characteristic Function Form By Song-Ju Kim; Taiki Takahashi; Kazuo Sano
  11. Data sharing games By V\'ictor Gallego; Roi Naveiro; David R\'ios Insua; Wolfram Rozas
  12. Partial Consensus in Large Games and Markets By Gabriel Desgranges; Sayantan Ghosal
  13. Competition in Signaling By Vaccari, Federico
  14. Port integration and competition under public and private ownership By Xu, Lili; Lee, Sang-Ho
  15. Entry Deterrence and Free Riding in License Auctions: Incumbent Heterogeneity and Monotonicity By Biung-Ghi Ju; Seung Han Yoo
  16. Data Brokers Co-Opetition By Yiquan Gu; Leonardo Madio; Carlo Reggiani
  17. Limited liability, strategic default and bargaining power By Balatti, Mirco; López-Quiles, Carolina
  18. Understanding algorithmic collusion with experience replay By Bingyan Han

  1. By: Masaki Aoyagi; Guillaume Frechette; Sevgi Yuksel
    Abstract: This paper uses a laboratory experiment to study beliefs and their relationship to action and strategy choices in finitely and indefinitely repeated prisoners' dilemma games. We find subjects' beliefs about the other player's action are accurate despite some systematic deviations corresponding to early pessimism in the indefinitely repeated game and late optimism in the finitely repeated game. The data reveals a close link between beliefs and actions that differs between the two games. In particular, the same history of play leads to different beliefs, and the same belief leads to different action choices in each game. Moreover, we find beliefs anticipate the evolution of behavior within a supergame, changing in response to the history of play (in both games) and the number of rounds played (in the finitely repeated game). We then use the subjects' beliefs over actions in each round to identify their beliefs over supergame strategies played by the other player. We find these beliefs correctly capture the different classes of strategies used in each game. Importantly, subjects using different strategies have different beliefs, and for the most part, strategies are subjectively rational given beliefs. The results also suggest subjects tend to overestimate the likelihood that others use the same strategy as them, while underestimating the likelihood that others use less cooperative strategies.
    Date: 2021–02
  2. By: Andrea Attar (TSE - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Eloisa Campioni (Unknown); Thomas Mariotti (Unknown); Gwenaël Piaser (Unknown)
    Abstract: We study competing-mechanism games under exclusive competition: principals first simultaneously post mechanisms, after which agents simultaneously choose to participate and communicate with at most one principal. In this setting, which is common to competing-auction and competitive-search applications, we develop two complete-information examples that question the relevance of the folk theorems for competing-mechanism games documented in the literature. The first example shows that there can exist pure-strategy equilibria in which some principal obtains a payoff below her min-max payoff, computed over all principals' decisions. Thus folk-theoremlike results may have to involve a bound on principals' payoffs that depends on the spaces of messages available to the agents, and not only on the players' actions. The second example shows that even this nonintrinsic approach is misleading when agents' participation decisions are strategic: there can exist incentive-feasible allocations in which principals obtain payoffs above their min-max payoffs, computed over arbitrary spaces of mechanisms, but which cannot be supported in equilibrium.
    Date: 2021
  3. By: Juan D. Moreno-Ternero (Department of Economics, Universidad Pablo de Olavide;); Min-Hung Tsay (Department of Economics, National Chung Cheng University); Chun-Hsien Yeh (Institute of Economics, Academia Sinica; Chung-Hua Institute for Economic Research)
    Abstract: We follow the Nash program to provide a new strategic justification for the TAL-family of rules for bankruptcy problems. The design of our game is inspired by an axiomatization of the TAL-family of rules exploiting the properties of consistency together with certain degrees of lower and upper bounds to all creditors. Bilateral negotiations of our game follow the spirit of those bounds. By means of consistency, we then extend the bilateral negotiations to an arbitrary number of creditors.
    Keywords: Nash program; bankruptcy problems; strategic justification; consistency; TAL-family of rules
    JEL: C71 C72 D63
    Date: 2021
  4. By: Ramakanta Patra (Department of Accounting, Economics and Finance, Cardiff Metropolitan University); Tadashi Sekiguchi (Institute of Economic Research, Kyoto University)
    Abstract: This paper studies an infinitely repeated duopoly game with incomplete information and with costly entry decisions. Every period, each player learns her private type and decides whether to pay a cost in order for her to enter or not. If she enters, she plays a game belonging to a class that includes Bertrand duopoly and some auction games as special cases, either as a monopolist or as a duopolist. The players can communicate before they make their entry decisions. We study full collusion (joint profit maximization) in this environment which requires a higher-quality player to solely enter and to choose an action maximizing the stage payoff. We present a condition on the stage game which is both necessary and sufficient in order for full collusion to be an equilibrium outcome for sufficiently patient players. The condition is more likely to hold when the entry cost increases, which signifies that the entry cost is an important factor facilitating full collusion. We also show that under some parameter restrictions, asymmetric equilibria where only one player reveals her type every period sustain full collusion for a wider range of discount factors. These asymmetric equilibria reduce the total amount of communication, which makes it harder for antitrust authorities to detect collusion.
    Keywords: Bertrand Competition; Fixed Costs; Unknown Costs; Private Information; Infinitely Repeated Game; Pre-play Communication; One-sided Communication; Full Collusion
    JEL: C73 D43 K21 L0
    Date: 2021–02
  5. By: Schauf, Andrew; Oh, Poong
    Abstract: When individuals extract benefits from multiple resources, the decision they face is twofold: besides choosing how much total effort to exert for extraction, they must also decide how to allocate this effort. We focus on the allocation aspect of this choice in an iterated game played on bipartite networks of agents and common-pool resources (CPRs) that degrade linearly in quality as extraction increases. When CPR users attempt to reallocate their extraction efforts among resources to maximize their own payoffs in the very next round (that is, myopically), collective wealth is increased. Using a heterogeneous mean-field approach, we estimate how these reallocations affect the payoffs of CPR users of different degrees within networks having different levels of degree heterogeneity. Focusing specifically on Nash equilibrium initial conditions, which represent the patterns of over-exploitation that result from rational extraction, we find that networks with greater heterogeneity among CPR degrees show greater improvements over equilibrium due to reallocation. When the marginal utility of extraction diminishes, these reallocations also reduce wealth inequality. These findings emphasize that CPR users’ adaptive reallocations of effort—a behavior that previously-studied network evolutionary game models typically disallow by construction—can serve to direct individuals’ self interest toward the collective good.
    Date: 2021–01–12
  6. By: Laohakunakorn, Krittanai; Levy, Gilat; Razin, Ronny
    Abstract: We analyze auctions when individuals have ambiguity over the joint information structures generating the valuations and signals of players. We analyze how two standard auction effects interact with the ambiguity of bidders over correlation structures. First, a “competition effect” arises when different beliefs about the correlation between bidders' valuations imply different likelihoods of facing competitive bids. Second, a “winner's value effect” arises when different beliefs imply different inferences about the winner's value. In the private values case, only the first effect exists and this implies that the distribution of bids first order stochastically dominates the distribution of bids in the absence of ambiguity. In common value auctions both effects exist and we show that compared to the canonical model, both in the first-price and second-price auctions, these effects combine to imply that the seller's revenue decreases with ambiguity (in contrast with the private values case). We then characterise the optimal auction in both the private and common value cases. A novel feature that arises in the optimal mechanism in the common values case is that the seller only partially insures the high type against ambiguity.
    Keywords: Ambiguity over correlation; Optimal auctions; Private and common value auctions
    JEL: D44 D81
    Date: 2019–11–01
  7. By: Shaun Hargreaves Heap; Mehmet S. Ismail
    Abstract: Rational players in game theory are neoliberal in the sense that they can choose any available action so as to maximize their payoffs. It is well known that this can result in Pareto inferior outcomes (e.g. the Prisoner's Dilemma). Classical liberalism, in contrast, argues that people should be constrained by a no-harm principle (NHP) when they act. We show, for the first time to the best of our knowledge, that rational players constrained by the NHP will produce Pareto efficient outcomes in n-person non-cooperative games. We also show that both rationality and the NHP are required for this result.
    Date: 2021–01
  8. By: Bettina Klaus
    Abstract: We consider a variation of the housing market model a la Shapley and Scarf (1974) where agents care both about their own consumption via demand preferences and about the agent who receives their endowment via supply preferences (see Klaus and Meo, 2021). Then, if preferences are either all demand lexicographic or all supply lexicographic, we characterize the corresponding top trading cycles rule by individual rationality, Pareto optimality, and strategy-proofness. Since on the lexicographic preference domains the strong core can be multi-valued, our result sheds light on the fact that the properties that also characterized the strong core rule for Shapley-Scarf housing markets (Ma, 1994) characterize the top trading cycles rule and not the strong core rule (or correspondence).
    Keywords: Core, characterization, externalities, housing markets, top trading cycles rule
    JEL: C70 C71 C78 D62 D64
    Date: 2021–02
  9. By: Masaki Aoyagi; Takehito Masuda; Naoko Nishimura
    Abstract: This paper uses laboratory experiments to study subjects' assessment of uncertainty resulting from strategic and non-strategic decisions of other players. Non-strategic events are defined by the colors of balls drawn from urns, whereas strategic events are defined by the action choice in Stag Hunt (SH) and Prisoners' Dilemma (PD) games. We elicit subjects' matching probabilities and examine if they satisfy the law of probability including monotonicity and additivity. Violations from the law are observed for both uncertainty sources, but are more substantial for strategic uncertainty. In particular, we observe a coordination fallacy, a violation of monotonicity whereby the probability weight placed on a symmetric coordination profile of the games exceeds that placed on the corresponding action choice. The violation is found to be severer for an efficient coordination profile.
  10. By: Song-Ju Kim; Taiki Takahashi; Kazuo Sano
    Abstract: In chaotic modern society, there is an increasing demand for the realization of true 'fairness'. In Greek mythology, Themis, the 'goddess of justice', has a sword in her right hand to protect society from vices, and a 'balance of judgment' in her left hand that measures good and evil. In this study, we propose a fair distribution method 'utilising physics' for the profit in games of characteristic function form. Specifically, we show that the linear programming problem for calculating 'nucleolus' can be efficiently solved by considering it as a physical system in which gravity works. In addition to being able to significantly reduce computational complexity thereby, we believe that this system could have flexibility necessary to respond to real-time changes in the parameter.
    Date: 2021–01
  11. By: V\'ictor Gallego; Roi Naveiro; David R\'ios Insua; Wolfram Rozas
    Abstract: Data sharing issues pervade online social and economic environments. To foster social progress, it is important to develop models of the interaction between data producers and consumers that can promote the rise of cooperation between the involved parties. We formalize this interaction as a game, the data sharing game, based on the Iterated Prisoner's Dilemma and deal with it through multi-agent reinforcement learning techniques. We consider several strategies for how the citizens may behave, depending on the degree of centralization sought. Simulations suggest mechanisms for cooperation to take place and, thus, achieve maximum social utility: data consumers should perform some kind of opponent modeling, or a regulator should transfer utility between both players and incentivise them.
    Date: 2021–01
  12. By: Gabriel Desgranges; Sayantan Ghosal
    Abstract: When is partial consensus compatible with equilibrium and when does it lead to non-equilibrium outcomes in large games and markets? In this paper, (a) we develop a new solution concept that allows for partial consensus about the outcomes of strategic and market interaction, and (b) an associated, continuous measure of the degree of stability, via belief coordination, for equilibrium outcomes. We differentiate the properties of our concepts from related notions developed elsewhere. In an economic application we examine the foundations of intertemporal trade via belief coordination in a two period economy and show that, under certain conditions, partial consensus over future prices is consistent with an asset price bubble.
    Keywords: p-consensus, p-stability, common knowledge, rationalizability, heterogeneous beliefs, coordination, games, markets
    JEL: C70 D84
    Date: 2021–02
  13. By: Vaccari, Federico
    Abstract: I study a multi-sender signaling game between an uninformed decision maker and two senders with common private information and opposed interests. Senders can misreport information at a cost that is tied to the size of the misrepresentation. The main results concern the amount of information that is transmitted in equilibrium and the language used by senders to convey such information. Fully revealing and pure strategy equilibria exist but are not plausible. I identify sufficient conditions under which equilibria always exist, are plausible, and essentially unique, and deliver a complete characterization of such equilibria. As an application, I study the informative value of different judicial procedures.
    Keywords: signaling, multi-sender, competition, misreporting, communication
    JEL: C72 D72 D82
    Date: 2021–02–12
  14. By: Xu, Lili; Lee, Sang-Ho
    Abstract: This study investigates the effect of port integration in a mixed oligopoly framework where a public port compete with private ports under price competition. We formulate two integration models, A-integration and B-integration, in which the public port integrates with its neighboring private port or with a non-adjacent private port, respectively. We demonstrate that the effects of A-integration (B-integration) will (not) depend on the gross consumer benefit of the cargo shipment B-integration always makes society better off. We then examine an endogenous port integration game and show that both integration and competition are Nash equilibria under the appropriate government side payments, while B-integration can be socially desirable under public finances.
    Keywords: Port integration; Mixed oligopoly; Public ownership; Private ownership; Endogenous port integration
    JEL: D43 L44 L91 R48
    Date: 2021–02
  15. By: Biung-Ghi Ju (Department of Economics, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, Republic of Korea, 08826); Seung Han Yoo (Department of Economics, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul, Republic of Korea, 02841)
    Abstract: We examine free riding for entry deterrence in license auctions with heterogeneous incumbents. We establish the monotonicity of randomized preemptive bidding equilibria: an incumbent with a higher entry-loss rate has greater free-riding incentive, choosing a lower deterring probability. We then identify conditions for the existence of a series of fully or partially participating equilibria such that two or more incumbents with bounded heterogeneity in their entry-loss rates participate in randomized preemptive bidding. As an application, we examine a simple case of a bipartite group of participating incumbents consisting of one "leader" and many "followers". We show that the policy of limiting the leader's participation (set-asides for entrants, limiting participation of incumbents with excessive market shares, etc.) may or may not increase entry probability.
    Keywords: entry deterrence, free-rider problem, asymmetric auctions
    JEL: D44 D47 L13
    Date: 2021
  16. By: Yiquan Gu; Leonardo Madio; Carlo Reggiani
    Abstract: Data brokers share consumer data with rivals and, at the same time, compete withthem for selling. We propose a “co-opetition” game of data brokers and characterisetheir optimal strategies. When data are “sub-additive” with the merged value netof the merging cost being lower than the sum of the values of individual datasets,data brokers are more likely to share their data and sell them jointly. When data are“super-additive”, with the merged value being greater than the sum of the individualdatasets, competition emerges more often. Finally, data sharing is more likely whendata brokers are more efficient at merging datasets than data buyers.
    Keywords: data brokers, consumer information, co-opetition, data sharing
    JEL: D43 L13 L86 M31
    Date: 2021–01
  17. By: Balatti, Mirco; López-Quiles, Carolina
    Abstract: In this paper we examine the effects of limited liability on mortgage dynamics. While the literature has focused on default rates, renegotiation, or loan rates individually, we study them together as equilibrium outcomes of the strategic interaction between lenders and borrowers. We present a simple model of default and renegotiation where the degree of limited liability plays a key role in agents' strategies. We then use Fannie Mae loan performance data to test the predictions of the model. We focus on Metropolitan Statistical Areas that are crossed by a State border in order to exploit the discontinuity in regulation around the borders of States. As predicted by the model, we find that limited liability results in higher default rates and renegotiation rates. Regarding loan pricing, while the model predicts higher interest rates for limited liability loans, we find no such evidence in the Fannie Mae data. We further investigate this by using loan application data, which contains the interest rates on loans sold to private vs public investors. We find that private investors do price in the difference in ex-ante predictable default risk for limited liability loans. JEL Classification: D10, E40, G21, R20, R30
    Keywords: debt repudiation, discontinuity, lender recourse, mortgage contracts, renegotiation
    Date: 2021–01
  18. By: Bingyan Han
    Abstract: In an infinitely repeated pricing game, pricing algorithms based on artificial intelligence (Q-learning) may consistently learn to charge supra-competitive prices even without communication. Although concerns on algorithmic collusion have arisen, little is known on underlying factors. In this work, we experimentally analyze the dynamics of algorithms with three variants of experience replay. Algorithmic collusion still has roots in human preferences. Randomizing experience yields prices close to the static Bertrand equilibrium and higher prices are easily restored by favoring the latest experience. Moreover, relative performance concerns also stabilize the collusion. Finally, we investigate the scenarios with heterogeneous agents and test robustness on various factors.
    Date: 2021–02

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