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on Game Theory |
| By: | Philippe Jehiel (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, UCL - University College of London [London]); Erik Mohlin (Lund University [Lund], Institute for Futures Studies) |
| Abstract: | We develop a framework for categorization in games, applicable both to multistage games of complete information and static games of incomplete information. Players use categories to form coarse beliefs about their opponents' behavior. Players best-respond given these beliefs, as in analogy-based expectations equilibria. Categories are related to previously used strategies via the requirements that categories contain a sufficient amount of observations and exhibit sufficient withincategory similarity, in line with the bias-variance trade-off. When applied to classic games including the chainstore game and adverse selection games our framework yields less unintuitive predictions than those arising with standard solution concepts. |
| Keywords: | Bounded rationality, Categorization, Bias-variance trade-off, Adverse selection, Chainstore paradox |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-04154272&r=gth |
| By: | Johannes Treutlein |
| Abstract: | Evidential cooperation in large worlds (ECL) refers to the idea that humans and other agents can benefit by cooperating with similar agents with differing values in causally disconnected parts of a large universe. Cooperating provides agents with evidence that other similar agents are likely to cooperate too, resulting in gains from trade for all. This could be a crucial consideration for altruists. I develop a game-theoretic model of ECL as an incomplete information bargaining problem. The model incorporates uncertainty about others' value systems and empirical situations, and addresses the problem of selecting a compromise outcome. Using the model, I investigate issues with ECL and outline open technical and philosophical questions. I show that all cooperators must maximize the same weighted sum of utility functions to reach a Pareto optimal outcome. However, I argue against selecting a compromise outcome implicitly by normalizing utility functions. I review bargaining theory and argue that the Nash bargaining solution could be a relevant Schelling point. I introduce dependency equilibria (Spohn 2007), an equilibrium concept suitable for ECL, and generalize a folk theorem showing that the Nash bargaining solution is a dependency equilibrium. I discuss gains from trade given uncertain beliefs about other agents and analyze how these gains decrease in several toy examples as the belief in another agent decreases. Finally, I discuss open issues in my model. First, the Nash bargaining solution is sometimes not coalitionally stable, meaning that a subset of cooperators can unilaterally improve payoffs by deviating from the compromise. I investigate conditions under which stable payoff vectors exist. Second, I discuss how to model agents' default actions without ECL. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.04879&r=gth |
| By: | Gentry, Matthew; Pesendorfer, Martin |
| Abstract: | A single-product retailer faces bargain hunting consumers whose willingness to pay incorporates sensations of gain and loss driven by differences between the observed price and prices they rationally expect in the spirit of Koszegi and Rabin (2006). We examine the Bayesian Nash equilibrium (non-commitment) pricing solution in which (i) the retailer maximizes profit given consumers' beliefs and (ii) consumers' beliefs are consistent with the retailer's choice. We show two novel results: First, a pure-strategy, uniform-price, equilibrium does not exist when consumers are bargain hunters who value gains more than losses. Second, in this case there exists a mixed strategy equilibrium and all mixed strategy equilibria involve the same retailer profit. The equilibrium retailer profit is (weakly) lower than in the absence of reference effects. |
| Keywords: | bargain hunting; pricing; reference effects |
| JEL: | J1 |
| Date: | 2021–09–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:111591&r=gth |
| By: | Olivier Compte |
| Abstract: | Motivated by the idea that lack of experience is a source of errors but that experience should reduce them, we model agents' behavior using a stochastic choice model, leaving endogenous the accuracy of their choice. In some games, increased accuracy is conducive to unstable best-response dynamics. We define the barrier to learning as the minimum level of noise which keeps the best-response dynamic stable. Using logit Quantal Response, this defines a limitQR Equilibrium. We apply the concept to centipede, travelers' dilemma, and 11-20 money-request games and to first-price and all-pay auctions, and discuss the role of strategy restrictions in reducing or amplifying barriers to learning. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.16904&r=gth |
| By: | Itai Arieli (Technion - Israel Institute of Technology); Ivan Geffner (Technion - Israel Institute of Technology); Moshe Tennenholtz (Technion - Israel Institute of Technology) |
| Abstract: | In an information aggregation game, a set of senders interact with a receiver through a mediator. Each sender observes the state of the world and communicates a message to the mediator, who recommends an action to the receiver based on the messages received. The payoff of the senders and of the receiver depend on both the state of the world and the action selected by the receiver. This setting extends the celebrated cheap talk model in two aspects: there are many senders (as opposed to just one) and there is a mediator. From a practical perspective, this setting captures platforms in which strategic experts advice is aggregated in service of action recommendations to the user. We aim at finding an optimal mediator/platform that maximizes the users' welfare given highly resilient incentive compatibility requirements on the equilibrium selected: we want the platform to be incentive compatible for the receiver/user when selecting the recommended action, and we want it to be resilient against group deviations by the senders/experts. We provide highly positive answers to this challenge, manifested through efficient algorithms. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.05054&r=gth |
| By: | Bingyan Han; Chi Seng Pun; Hoi Ying Wong |
| Abstract: | This paper studies robust time-inconsistent (TIC) linear-quadratic stochastic control problems, formulated by stochastic differential games. By a spike variation approach, we derive sufficient conditions for achieving the Nash equilibrium, which corresponds to a time-consistent (TC) robust policy, under mild technical assumptions. To illustrate our framework, we consider two scenarios of robust mean-variance analysis, namely with state- and control-dependent ambiguity aversion. We find numerically that with time inconsistency haunting the dynamic optimal controls, the ambiguity aversion enhances the effective risk aversion faster than the linear, implying that the ambiguity in the TIC cases is more impactful than that under the TC counterparts, e.g., expected utility maximization problems. |
| Date: | 2023–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2306.16982&r=gth |
| By: | Krishnamurthy Iyer; Haifeng Xu; You Zu |
| Abstract: | We consider a dynamic Bayesian persuasion setting where a single long-lived sender persuades a stream of ``short-lived'' agents (receivers) by sharing information about a payoff-relevant state. The state transitions are Markovian and the sender seeks to maximize the long-run average reward by committing to a (possibly history-dependent) signaling mechanism. While most previous studies of Markov persuasion consider exogenous agent beliefs that are independent of the chain, we study a more natural variant with endogenous agent beliefs that depend on the chain's realized history. A key challenge to analyze such settings is to model the agents' partial knowledge about the history information. We analyze a Markov persuasion process (MPP) under various information models that differ in the amount of information the receivers have about the history of the process. Specifically, we formulate a general partial-information model where each receiver observes the history with an $\ell$ period lag. Our technical contribution start with analyzing two benchmark models, i.e., the full-history information model and the no-history information model. We establish an ordering of the sender's payoff as a function of the informativeness of agent's information model (with no-history as the least informative), and develop efficient algorithms to compute optimal solutions for these two benchmarks. For general $\ell$, we present the technical challenges in finding an optimal signaling mechanism, where even determining the right dependency on the history becomes difficult. To bypass the difficulties, we use a robustness framework to design a "simple" \emph{history-independent} signaling mechanism that approximately achieves optimal payoff when $\ell$ is reasonably large. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.03181&r=gth |
| By: | Philippe Jehiel (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, UCL - University College of London [London]); Giacomo Weber (PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, PJSE - Paris Jourdan Sciences Economiques - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement) |
| Abstract: | Families of normal-form two-player games are categorized by players into K analogy classes applying the K-means clustering technique to the data generated by the distributions of opponent's behavior. This results in Calibrated Analogy-Based Expectation Equilibria in which strategies are analogy-based expectation equilibria given the analogy partitions and analogy partitions are derived from the strategies by the K-means clustering algorithm. We discuss various concepts formalizing this, and observe that distributions over analogy partitions are sometimes required to guarantee existence. Applications to games with linear best-responses are discussed highlighting the differences between strategic complements and strategic substitutes. |
| Keywords: | K-mean clustering, Analogy-based Expectation Equilibrium K-mean clustering |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:halshs-04154234&r=gth |
| By: | Benjamin Ouvrard (GAEL - Laboratoire d'Economie Appliquée de Grenoble - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes); Arnaud Reynaud (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - 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); Stéphane Cezera (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - 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); Alban Thomas (UMR PSAE - Paris-Saclay Applied Economics - AgroParisTech - Université Paris-Saclay - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, US ODR - Observatoire des Programmes Communautaires de Développement Rural - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement); Dishant Jojit James (Wyzsza Szkola Bankowa University); Murudaiah Shivamurthy (Department of Agricultural Extension, GKVK, UAS, Bangalore) |
| Abstract: | We use a framed-field experiment to analyze the preferences of Indian farmers regarding water sharing. Farmers play a dictator game (DG) behind the veil of ignorance in which a limited quantity of water has to be allocated between two farmers. We vary the equity/efficiency trade-off by introducing some heterogeneity between farmers' productivity and by considering an upstream/downstream spatial configuration. We first show that generosity in the DG is high (on average, respectively 44% and 47% of the total quantity of water or the total profit are left by the dictator). Only a small proportion of farmers act in the DG as selfish profit maximizers, a majority of them adopting efficient, egalitarian in payoff or egalitarian in quantity behaviors. We then show that it is possible to induce more efficient water allocation behaviors in the DG by modifying farmer's choice architecture. A loss framing induces farmers to share more efficiently the water resource, but only when the most productive farmer is located downstream. On the contrary, we find mild evidence that farmers choose less often the efficient solution with a gain framing. |
| Keywords: | Dictator Game, Framed-field experiment, Framing, Water sharing |
| Date: | 2023–07–04 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-04150233&r=gth |
| By: | Nicola Campigotto; Marco Catola; Simone D’Alessandro; Pietro Guarnieri; Lorenzo Spadoni |
| Abstract: | This paper explores the potential of voluntary consumption quotas as a strategy to address resource supply shortages. The results of an incentivized online experiment are presented in which a Nash demand game was used to model an energy consumption problem. Participants had the option to join an energy conservation programme by accepting a consumption quota. Those who accepted the quota traded off their maximum demand for energy in exchange for the certainty that their demand would be met, while those who rejected the quota could demand and possibly earn more but risked suffering from a power outage, in which case they received nothing. Three different quota schemes are examined, and their policy implications are discussed. Our findings suggest that voluntary quotas may lead to a significant decrease in overall demand and contribute to enhancing consumption security. |
| Keywords: | energy consumption, online experiment, Nash demand game, power outages, voluntary quotas |
| JEL: | C72 C99 Q48 |
| Date: | 2023–07–01 |
| URL: | http://d.repec.org/n?u=RePEc:pie:dsedps:2023/299&r=gth |
| By: | Mignot, Sarah; Tramontana, Fabio; Westerhoff, Frank H. |
| Abstract: | We develop a nonlinear duopoly model in which the heuristic expectation formation and learning behavior of two boundedly rational firms may engender complex dynamics. Most importantly, we assume that the firms employ different forecasting models to predict the behavior of their opponent. Moreover, the firms learn by leaning more strongly on forecasting models that yield more precise predictions. An eight-dimensional nonlinear map drives the dynamics of our approach. We analytically derive the conditions under which its unique steady state is locally stable and numerically study its out-of-equilibrium behavior. In doing so, we detect multiple scenarios with coexisting attractors at which the firms' behavior yields distinctively different market outcomes. |
| Keywords: | Duopoly model, heuristic expectation formation, learning behavior, nonlinear dynamics, stability and bifurcation analysis, coexisting attractors |
| JEL: | C73 D43 L12 |
| Date: | 2023 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:bamber:187&r=gth |
| By: | Tirole, Jean; Moisson, Paul-Henri; Dubois, Pierre |
| Abstract: | It is puzzling that cooperatives, which stand for the interests of their users, do not occupy more space in the market for corporate forms. This paper unveils a new impediment to their formation. It shows that equilibrium free-riding handicaps cooperatives in their competition with alternative institutions, notably the for-profits. The irrelevance of cooperatives is a remarkably robust result. The paper then analyzes desirable government interventions in the corporate market. |
| Keywords: | Cooperatives; free-riding; competing corporate forms |
| JEL: | D23 D71 D8 L22 |
| Date: | 2023–07–03 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:128186&r=gth |
| By: | Qian Lei; Chi Seng Pun |
| Abstract: | This paper studies the well-posedness of a class of nonlocal parabolic partial differential equations (PDEs), or equivalently equilibrium Hamilton-Jacobi-Bellman equations, which has a strong tie with the characterization of the equilibrium strategies and the associated value functions for time-inconsistent stochastic control problems. Specifically, we consider nonlocality in both time and space, which allows for modelling of the stochastic control problems with initial-time-and-state dependent objective functionals. We leverage the method of continuity to show the global well-posedness within our proposed Banach space with our established Schauder prior estimate for the linearized nonlocal PDE. Then, we adopt a linearization method and Banach's fixed point arguments to show the local well-posedness of the nonlocal fully nonlinear case, while the global well-posedness is attainable provided that a very sharp a-priori estimate is available. On top of the well-posedness results, we also provide a probabilistic representation of the solutions to the nonlocal fully nonlinear PDEs and an estimate on the difference between the value functions of sophisticated and na\"{i}ve controllers. Finally, we give a financial example of time inconsistency that is proven to be globally solvable. |
| Date: | 2023–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2307.01986&r=gth |