nep-gth New Economics Papers
on Game Theory
Issue of 2023‒03‒13
fifteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Computing Perfect Stationary Equilibria in Stochastic Games By Li, Peixuan; Dang, Chuangyin; Herings, Jean-Jacques
  2. Affective interdependence and welfare By Heifetz, Aviad; Minelli, Enrico; Polemarchakis, Herakles
  3. Signaling Games with Costly Monitoring By Reuben Bearman
  4. An Experiment on The Nash Program: A Comparison of Two Strategic Mechanisms Implementing the Shapley Value By Michela Chessa; Nobuyuki Hanaki; Aymeric Lardon; Takashi Yamada
  5. Dynamic Programming for Pure-Strategy Subgame Perfection in an Arbitrary Game By Peter A. Streufert
  6. A Group Public Goods Game with Position Uncertainty By Sakib Anwar, Chowdhury Mohammad; Bruno, Jorge; SenGupta, Sonali
  7. Full Surplus Extraction from Colluding Bidders By Daniil Larionov
  8. Learning in Rent-Seeking Contests with Payoff Risk and Foregone Payoff Information By Aidas Masiliūnas
  9. Informationally Robust Cheap-Talk By Itai Arieli; Ronen Gradwohl; Rann Smorodinsky
  10. Persuading a Behavioral Agent: Approximately Best Responding and Learning By Yiling Chen; Tao Lin
  11. Strategic choice of price-setting algorithms By Buchali, Katrin; Grüb, Jens; Muijs, Matthias; Schwalbe, Ulrich
  12. The Hazards and Benefits of Condescension in Social Learning By Itai Arieli; Yakov Babichenko; Stephan M\"uller; Farzad Pourbabaee; Omer Tamuz
  13. The Tripartite Auction Folk Theorem By David K Levine; Andrea Mattozzi; Salvatore Modica
  14. Reversal of Bertrand-Cournot Ranking for Optimal Privatization Level By Paul, Arindam; De, Parikshit
  15. Selling Data to a Competitor By Ronen Gradwohl; Moshe Tennenholtz

  1. By: Li, Peixuan; Dang, Chuangyin; Herings, Jean-Jacques (Tilburg University, School of Economics and Management)
    Date: 2023
  2. By: Heifetz, Aviad (Open University Tel Aviv); Minelli, Enrico (University of Brescia); Polemarchakis, Herakles (University of Warwick)
    Abstract: Purely affective interaction allows the welfare of an individual to depend on her own actions and on the profile of welfare levels of others. Under an assumption on the structure of mutual affection that we interpret as nonexplosive mutual affection, we show that equilibria of simultaneous-move affective interaction are Pareto optimal independently of whether or not an induced standard game exists. Moreover, if purely affective interaction induces a standard game, then an equilibrium profile of actions is a Nash equilibrium of the game, and this Nash equilibrium and Pareto optimal profile of strategies is locally dominan
    Keywords: purely affective interactions ; Pareto optimality JEL codes: D62
    Date: 2023
  3. By: Reuben Bearman
    Abstract: If in a signaling game the receiver expects to gain no information by monitoring the signal of the sender, then when a cost to monitor is implemented he will never pay that cost regardless of his off-path beliefs. This is the argument of a recent paper by T. Denti (2021). However, which pooling equilibrium does a receiver anticipate to gain no information through monitoring? This paper seeks to prove that given a sufficiently small cost to monitor any pooling equilibrium with a non-zero index will survive close to the original equilibrium.
    Date: 2023–02
  4. By: Michela Chessa; Nobuyuki Hanaki; Aymeric Lardon; Takashi Yamada
    Abstract: We experimentally compare two well-known mechanisms inducing the Shapley value as an ex ante equilibrium outcome of a noncooperative bargaining procedure: the demand-based Winter’s demand commitment bargaining mechanism and the offer-based Hart and Mas-Colell procedure. Our results suggest that the offer-based Hart and Mas-Colell mechanism better induces players to cooperate and to agree on an efficient outcome, whereas the demand-based Winter mechanism better implements allocations that reflect players' effective power, provided that the grand coalition is formed.
    Date: 2022–05
  5. By: Peter A. Streufert
    Abstract: This paper uses value functions to characterize the pure-strategy subgame-perfect equilibria of an arbitrary, possibly infinite-horizon game. It specifies the game's extensive form as a pentaform (Streufert 2023p, coming revision of arXiv:2107.10801), which is a set of quintuples formalizing the abstract relationships between nodes, actions, players, and situations (situations generalize information sets). Because a pentaform is a set, this paper can explicitly partition the game form into piece forms, each of which starts at a (Selten) subroot and contains all subsequent nodes except those that follow a subsequent subroot. Then the set of subroots becomes the domain of a value function, and the piece-form partition becomes the framework for a value recursion which generalizes the Bellman equation from dynamic programming. The main results connect the value recursion with the subgame-perfect equilibria of the original game, under the assumptions of upper- and lower-convergence. Finally, a corollary characterizes subgame perfection as the absence of an improving one-piece deviation.
    Date: 2023–02
  6. By: Sakib Anwar, Chowdhury Mohammad (BLDT, University of Winchester); Bruno, Jorge (BLDT, University of Winchester); SenGupta, Sonali (Queens Management School, Queen’s University Belfast.)
    Abstract: We model a dynamic public good contribution game, where players are (naturally) formed into groups. The groups are exogenously placed in a sequence, with limited information available to players about their groups’ position in the sequence. Contribution decisions are made by players simultaneously and independently, and the groups’ total contribution is made sequentially. We try to capture both inter and intra-group behaviors and analyze different situations where players observe partial history about total contributions of their predecessor groups. Given this framework, we show that even when players observe a history of defection (no contribution), a cooperative outcome is achievable. This is particularly interesting in the situation when players observe only their immediate predecessor groups’ contribution, where we observe that players play an important role in motivating others to contribute.
    Keywords: Social Dilemmas ; Public Goods ; Position Uncertainty ; Voluntary Contributions ; Fundraising ; Groups JEL codes: C72; D82; H41
    Date: 2022
  7. By: Daniil Larionov
    Abstract: I consider a repeated auction setting with colluding buyers and a seller who adjusts reserve prices over time without long-term commitment. To model the seller’s concern for collusion, I introduce a new equilibrium concept: collusive public perfect equilibrium (cPPE). For every strategy of the seller I define the corresponding “buyer-game†in which the seller is replaced by Nature who chooses the reserve prices for the buyers in accordance with the seller’s strategy. A public perfect equilibrium is collusive if the buyers cannot achieve a higher symmetric public perfect equilibrium payoff in the corresponding buyer-game. In a setting with symmetric buyers with private binary iid valuations and publicly revealed bids, I find a collusive public perfect equilibrium that allows the seller to extract the entire surplus from the buyers in the limit as the discount factor goes to 1. I therefore show that a patient, non-committed seller can effectively fight collusion even when she can only set reserve prices and has to satisfy stringent public disclosure requirements.
    Keywords: Repeated Auctions, Auction Design, Collusion, Full Surplus Extraction
    JEL: D44 D47 C73
    Date: 2023–02
  8. By: Aidas Masiliūnas (Department of Economics, University of Sheffield, 9 Mappin Street, Sheffield S1 4DT, UK.)
    Abstract: We test whether deviations from Nash equilibrium in rent-seeking contests can be explained by the slow convergence of payoff-based learning. We identify and eliminate two noise sources that slow down learning: first, opponents are changing their actions across rounds; second, payoffs are probabilistic, which reduces the correlation between expected and realized payoffs. We find that average choices are not significantly different from the risk-neutral Nash equilibrium predictions only when both noise sources are eliminated by supplying foregone payoff information and removing payoff risk. Payoff-based learning can explain these results better than alternative theories. We propose a hybrid learning model that combines reinforcement and belief learning with risk, social and other preferences, and show that it fits data well, mostly because of reinforcement learning.
    Keywords: experiment, contests, reinforcement learning, foregone payoffs, payoff risk, Nash equilibrium
    JEL: C72 C91 D71 D81
    Date: 2023–01
  9. By: Itai Arieli; Ronen Gradwohl; Rann Smorodinsky
    Abstract: We study the robustness of cheap-talk equilibria to infinitesimal private information of the receiver in a model with a binary state-space and state-independent sender-preferences. We show that the sender-optimal equilibrium is robust if and only if this equilibrium either reveals no information to the receiver or fully reveals one of the states with positive probability. We then characterize the actions that can be played with positive probability in any robust equilibrium. Finally, we fully characterize the optimal sender-utility under binary receiver's private information, and provide bounds for the optimal sender-utility under general private information.
    Date: 2023–02
  10. By: Yiling Chen; Tao Lin
    Abstract: The classic Bayesian persuasion model assumes a Bayesian and best-responding receiver. We study a relaxation of the Bayesian persuasion model where the receiver can approximately best respond to the sender's signaling scheme. We show that, under natural assumptions, (1) the sender can find a signaling scheme that guarantees itself an expected utility almost as good as its optimal utility in the classic model, no matter what approximately best-responding strategy the receiver uses; (2) on the other hand, there is no signaling scheme that gives the sender much more utility than its optimal utility in the classic model, even if the receiver uses the approximately best-responding strategy that is best for the sender. Together, (1) and (2) imply that the approximately best-responding behavior of the receiver does not affect the sender's maximal achievable utility a lot in the Bayesian persuasion problem. The proofs of both results rely on the idea of robustification of a Bayesian persuasion scheme: given a pair of the sender's signaling scheme and the receiver's strategy, we can construct another signaling scheme such that the receiver prefers to use that strategy in the new scheme more than in the original scheme, and the two schemes give the sender similar utilities. As an application of our main result (1), we show that, in a repeated Bayesian persuasion model where the receiver learns to respond to the sender by some algorithms, the sender can do almost as well as in the classic model. Interestingly, unlike (2), with a learning receiver the sender can sometimes do much better than in the classic model.
    Date: 2023–02
  11. By: Buchali, Katrin; Grüb, Jens; Muijs, Matthias; Schwalbe, Ulrich
    Abstract: Recent experimental simulations have shown that autonomous pricing algorithms are able to learn collusive behavior and thus charge supra-competitive prices without being explicitly programmed to do so. These simulations assume, however, that both firms employ the identical price-setting algorithm based on Q-learning. Thus, the question arises whether the underlying assumption that both firms employ a Q-learning algorithm can be supported as an equilibrium in a game where firms can chose between different pricing rules. Our simulations show that when both firms use a learning algorithm, the outcome is not an equilibrium when alternative price setting rules are available. In fact, simpler price setting rules as for example meeting competition clauses yield higher payoffs compared to Q-learning algorithms.
    Keywords: pricing algorithms, algorithmic collusion, reinforcement learning
    JEL: D43 D83 L13 L49
    Date: 2023
  12. By: Itai Arieli; Yakov Babichenko; Stephan M\"uller; Farzad Pourbabaee; Omer Tamuz
    Abstract: In a misspecified social learning setting, agents are condescending if they perceive their peers as having private information that is of lower quality than it is in reality. Applying this to a standard sequential model, we show that outcomes improve when agents are mildly condescending. In contrast, too much condescension leads to bad outcomes, as does anti-condescension.
    Date: 2023–01
  13. By: David K Levine; Andrea Mattozzi; Salvatore Modica
    Date: 2023–02–18
  14. By: Paul, Arindam; De, Parikshit
    Abstract: We consider a vertically related differentiated product mixed duopoly market where a public and private firm compete in the downstream market. The public firm is partially privatized and a welfare maximizing regulator chooses the privatization level. The production of the final commodity requires a key input that is supplied by a foreign monopolist who in the upstream market can practice either uniform or discriminatory pricing. We show that with uniform pricing regime the privatization is always larger under Cournot competition while in case of discriminatory pricing regime, the privatization level under Bertrand competition is always larger. We also find that under discriminatory pricing regime, the Cournot-Bertrand ranking of other relevant variables are sensitive to the degree of substitutability.
    Keywords: D4, D6, H4, L1, L2
    JEL: L1 L2
    Date: 2022–09–15
  15. By: Ronen Gradwohl; Moshe Tennenholtz
    Abstract: We study the costs and benefits of selling data to a competitor. Although selling all consumers' data may decrease total firm profits, there exist other selling mechanisms -- in which only some consumers' data is sold -- that render both firms better off. We identify the profit-maximizing mechanism, and show that the benefit to firms comes at a cost to consumers. We then construct Pareto-improving mechanisms, in which each consumers' welfare, as well as both firms' profits, increase. Finally, we show that consumer opt-in can serve as an instrument to induce firms to choose a Pareto-improving mechanism over a profit-maximizing one.
    Date: 2023–02

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