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on Game Theory |
| By: | Décamps, Jean-Paul; Gensbittel, Fabien; Mariotti, Thomas |
| Abstract: | We study a generic family of two-player continuous-time nonzero-sum stopping games modeling a war of attrition with symmetric information and stochastic payoffs that depend on an homogeneous linear diffusion. We first show that any Markovian mixed strategy for player i can be represented by a pair (µ i , S i ), where µ i is a measure over the state space representing player i’s stopping intensity, and S i is a subset of the state space over which player i tops with probability 1. We then prove that, if players are asymmetric, then, in all mixed-strategy Markov-perfect equilibria, the measures µ i have to be essentially discrete, and we characterize any such equilibrium through a variational system satisfied by the players’ equilibrium value functions. This result contrasts with the literature, which focuses on pure-strategy equilibria, or, in the case of symmetric players, on mixed-strategy equilibria with absolutely continuous stopping intensities. We illustrate this result by revisiting the model of exit in a duopoly under uncertainty, and exhibit a mixed-strategy equilibrium in which attrition takes place on the equilibrium path though firms have different liquidation values. |
| Keywords: | War of Attrition; Mixed-Strategy Equilibrium; Uncertainty. |
| JEL: | C61 D25 D83 |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:127448&r= |
| By: | Frédéric Koessler (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); Marie Laclau (HEC Paris - Ecole des Hautes Etudes Commerciales, GREGHEC - Groupement de Recherche et d'Etudes en Gestion - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, CNRS - Centre National de la Recherche Scientifique); Jérôme Renault (TSE-R - Toulouse School of Economics - UT1 - Université Toulouse 1 Capitole - Université Fédérale Toulouse Midi-Pyrénées - 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); Tristan Tomala (GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC - HEC Paris - Ecole des Hautes Etudes Commerciales - CNRS - Centre National de la Recherche Scientifique, HEC Paris - Ecole des Hautes Etudes Commerciales) |
| Abstract: | We analyze information design games between two designers with opposite preferences and a single agent. Before the agent makes a decision, designers repeatedly disclose public information about persistent state parameters. Disclosure continues until no designer wishes to reveal further information. We consider environments with general constraints on feasible information disclosure policies. Our main results characterize equilibrium payoffs and strategies of this long information design game and compare them with the equilibrium outcomes of games where designers move only at a single predetermined period. When information disclosure policies are unconstrained, we show that at equilibrium in the long game, information is revealed right away in a single period; otherwise, the number of periods in which information is disclosed might be unbounded. As an application, we study a competition in product demonstration and show that more information is revealed if each designer could disclose information at a predetermined period. The format that provides the buyer with most information is the sequential game where the last mover is the ex-ante favorite seller. |
| Keywords: | Bayesian persuasion,Concavification,Convexification,Information design,Mertens Zamir solution,Product demonstration,Splitting games,Statistical experiments,Stochastic games |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:halshs-02400053&r= |
| By: | Dean P. Foster; Sergiu Hart |
| Abstract: | We propose to smooth out the calibration score, which measures how good a forecaster is, by combining nearby forecasts. While regular calibration can be guaranteed only by randomized forecasting procedures, we show that smooth calibration can be guaranteed by deterministic procedures. As a consequence, it does not matter if the forecasts are leaked, i.e., made known in advance: smooth calibration can nevertheless be guaranteed (while regular calibration cannot). Moreover, our procedure has finite recall, is stationary, and all forecasts lie on a finite grid. To construct the procedure, we deal also with the related setups of online linear regression and weak calibration. Finally, we show that smooth calibration yields uncoupled finite-memory dynamics in n-person games "smooth calibrated learning" in which the players play approximate Nash equilibria in almost all periods (by contrast, calibrated learning, which uses regular calibration, yields only that the time-averages of play are approximate correlated equilibria). |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.07152&r= |
| By: | Cécile Bazart (CEE-M - Centre d'Economie de l'Environnement - Montpellier - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement - Institut Agro Montpellier - Institut Agro - Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement - UM - Université de Montpellier); Mathieu Lefebvre (AMSE - Aix-Marseille Sciences Economiques - EHESS - École des hautes études en sciences sociales - AMU - Aix Marseille Université - ECM - École Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique); Julie Rosaz (BSB - Burgundy School of Business (BSB) - Ecole Supérieure de Commerce de Dijon Bourgogne (ESC), CEREN - Centre de Recherche sur l'ENtreprise [Dijon] - BSB - Burgundy School of Business (BSB) - Ecole Supérieure de Commerce de Dijon Bourgogne (ESC)) |
| Abstract: | Through a series of experiments, this paper tests the relative efficiency of persuasion and commitment schemes to increase and sustain contribution levels in a Voluntary Contribution Game. The design allows us to compare a baseline consisting of a repeated public good game to four treatments of the same game in which we successively introduce a persuasion message, commitment devices, and communication between subjects. Our results suggest that these non-monetary procedures significantly increase cooperation and reduce the decay of contributions across periods. |
| Keywords: | Communication,Persuasion,Commitment,Voluntary contribution mechanism |
| Date: | 2022–12 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-03777675&r= |
| By: | Saglam, Ismail |
| Abstract: | This paper studies the incentives for, and the welfare effects of, pre-donation in a vertically related industry where two downstream firms that produce a homogenous good jointly bargain, using the generalized Nash rule, with an upstream firm over a linear input price before they engage in Cournot competition. We theoretically show that the downstream industry has no incentive to make any pre-donation and this is irrespective of its bargaining power. We also show computationally that (i) the upstream firm finds to make unilateral pre-donation optimal if and only if its bargaining power is sufficiently small and (ii) its optimal pre-donation (whenever positive) always yields Pareto welfare gains. |
| Keywords: | Vertically related industry; Nash bargaining; pre-donation. |
| JEL: | C78 L12 L13 L22 |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:114835&r= |
| By: | Panagiotis Kyriazis; Edmund Lou |
| Abstract: | How important are leaders' actions in facilitating coordination? In this paper, we investigate their signaling role in a global games framework. A perfectly informed leader and a team of followers face a coordination problem. Despite the endogenous information generated by the leader's action, we provide a necessary and sufficient condition that makes the monotone equilibrium strategy profile uniquely $\Delta$-rationalizable and hence guarantees equilibrium uniqueness. Moreover, the unique equilibrium is fully efficient. This result remains valid when the leader observes a noisy signal about the true state except full efficiency may not be obtained. We discuss the implications of our results for a broad class of phenomena such as adoption of green technology, currency attacks and revolutions. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.12426&r= |
| By: | Masaaki Fujii |
| Abstract: | In this work, we develop an equilibrium model for price formation of securities in a market composed of two populations of different types: the first one consists of cooperative agents, while the other one consists of non-cooperative agents. The trading of every cooperative member is assumed to be coordinated by a central planner. In the large population limit, the problem for the central planner is shown to be a conditional extended mean-field control. In addition to the convexity assumptions, if the relative size of the cooperative population is small enough, then we are able to show the existence of a unique equilibrium for both the finite-agent and the mean-field models. The strong convergence to the mean-field model is also proved under the same conditions. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.12639&r= |
| By: | Dean P. Foster; Sergiu Hart |
| Abstract: | Calibration means that forecasts and average realized frequencies are close. We develop the concept of forecast hedging, which consists of choosing the forecasts so as to guarantee that the expected track record can only improve. This yields all the calibration results by the same simple basic argument while differentiating between them by the forecast-hedging tools used: deterministic and fixed point based versus stochastic and minimax based. Additional contributions are an improved definition of continuous calibration, ensuing game dynamics that yield Nash equilibria in the long run, and a new calibrated forecasting procedure for binary events that is simpler than all known such procedures. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.07169&r= |
| By: | Alessandro Micheli; Eyal Neuman |
| Abstract: | We consider a stochastic game between a slow institutional investor and a high-frequency trader who are trading a risky asset and their aggregated order-flow impacts the asset price. We model this system by means of two coupled stochastic control problems, in which the high-frequency trader exploits the available information on a price predicting signal more frequently, but is also subject to periodic "end of day" inventory constraints. We first derive the optimal strategy of the high-frequency trader given any admissible strategy of the institutional investor. Then, we solve the problem of the institutional investor given the optimal signal-adaptive strategy of the high-frequency trader, in terms of the resolvent of a Fredholm integral equation, thus establishing the unique multi-period Stackelberg equilibrium of the game. Our results provide an explicit solution to the game, which shows that the high-frequency trader can adopt either predatory or cooperative strategies in each period, depending on the tradeoff between the order-flow and the trading signal. We also show that the institutional investor's strategy is considerably more profitable when the order-flow of the high-frequency trader is taken into account in her trading strategy. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.01901&r= |
| By: | Nelson Vadori; Leo Ardon; Sumitra Ganesh; Thomas Spooner; Selim Amrouni; Jared Vann; Mengda Xu; Zeyu Zheng; Tucker Balch; Manuela Veloso |
| Abstract: | We study a game between liquidity provider and liquidity taker agents interacting in an over-the-counter market, for which the typical example is foreign exchange. We show how a suitable design of parameterized families of reward functions coupled with associated shared policy learning constitutes an efficient solution to this problem. Precisely, we show that our deep-reinforcement-learning-driven agents learn emergent behaviors relative to a wide spectrum of incentives encompassing profit-and-loss, optimal execution and market share, by playing against each other. In particular, we find that liquidity providers naturally learn to balance hedging and skewing as a function of their incentives, where the latter refers to setting their buy and sell prices asymmetrically as a function of their inventory. We further introduce a novel RL-based calibration algorithm which we found performed well at imposing constraints on the game equilibrium, both on toy and real market data. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.07184&r= |
| By: | Paan Jindapon; Pacharasut Sujarittanonta; Ajalavat Viriyavipart |
| Abstract: | We propose a framework to analyze the effects of income correlation between two players on risk sharing without commitment. In theory, the likelihood that a risk-sharing agreement is self-enforcing decreases with income correlation. We tested this prediction in the laboratory with negative, zero, and positive correlation coefficients and observed the largest average transfer in the positive-correlation treatment. This surprising result suggests that experiencing the same state of income could create a social bond and induce altruism between the two players. Therefore, informal risk sharing can be successful in a group with social identity despite high income interdependence. |
| Keywords: | Risk sharing; Income correlation; Infinite horizon games; Income smoothing; Altruism; Economic experiments |
| JEL: | D81 C91 C73 O17 |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:pui:dpaper:191&r= |
| By: | Rama,Martin G.; Li,Yue |
| Abstract: | Institutional weaknesses limit the capacity of local governments to support efficienturbanization in developing countries. They also lead to the emergence of large developers with the clout to build entirecities. This paper analyzes the urbanization process when local governments are weak and large developers arepowerful. Results from a non-cooperative game setting with minimal assumptions show that multiple equilibria can emergedepending on key institutional parameters of the model and the nature of the game, but all of them are inefficient. Inthis simple setting, increasing the capacity of the local government may not lead to better outcomes, because it maycrowd out urban land development by the more effective private investor. Subsidizing the large investor can ensureefficiency, but it makes the rest of society worse off. Selling the rights to the city can be Pareto efficient, butonly provided that the price at which the rights are sold are sufficiently high. However, more analytical andempirical work is needed before these analyses can be deemed relevant in practice. Competition among jurisdictions, timeconsistency challenges, and the social implications of private cities deserve special attention. |
| Keywords: | Regional Urban Development,National Urban Development Policies & Strategies,Urban Communities,City to City Alliances,Urban Economic Development,Urban Economics,Private Sector Economics,Legal Products,Regulatory Regimes,Legislation,Legal Reform,Judicial System Reform,Social Policy,Common Property Resource Development,Transport Services |
| Date: | 2022–02–10 |
| URL: | http://d.repec.org/n?u=RePEc:wbk:wbrwps:9936&r= |
| By: | Dimova, Ralitza (University of Manchester); Abou, Edouard Pokou (Jean Lorougnon Guede University); Basu, Arnab K. (Cornell University); Viennet, Romane (OECD) |
| Abstract: | Is the impact of women's bargaining power on the welfare of the household always positive? We address this question by developing a novel experimental measure of bargaining power over family expenditures in Ivory Coast and studying its determinants. We find that men prioritise food expenditures, women prioritise the transfers to parents and the two of them show similar revealed preferences with respect to educational expenditures. The bargaining power of the woman over the three categories of expenditures of interest is correlated with the education of the wife, the income of the husband and the bride price. The results contribute to the debate on the superior concern of the woman about child welfare and could have interesting policy implications. |
| Keywords: | bargaining power, public goods games, revealed preferences, Côte d'Ivoire |
| JEL: | C93 J43 O55 |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp15583&r= |
| By: | Armel Jacques |
| Date: | 2022 |
| URL: | http://d.repec.org/n?u=RePEc:tep:teppwp:wp22-14&r= |
| By: | Mehmet S. Ismail |
| Abstract: | In this note, I study the institutions and game theoretic assumptions that would prevent the emergence of "superhuman-level" arfiticial general intelligence, denoted by AI*. These assumptions are (i) the "Freedom of the Mind," (ii) open source "access" to AI*, and (iii) rationality of the representative human agent, who competes against AI*. I prove that under these three assumptions it is impossible that an AI* exists. This result gives rise to two immediate recommendations for public policy. First, "cloning" digitally the human brain should be strictly regulated, and hypothetical AI*'s access to brain should be prohibited. Second, AI* research should be made widely, if not publicly, accessible. |
| Date: | 2022–09 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2209.12346&r= |
| By: | Devarajan,Shantayanan; Do,Quy-Toan |
| Abstract: | Why is governance in resource-rich countries so poor This paper argues that it is becausegovernments in these countries do not rely on taxation, which is an important instrument for citizens to hold theirgovernments accountable. Using a game-theoretic model, the authors show that the combination of low taxes and weakgovernance can be an equilibrium in an economy with sizeable mineral revenues. As income from natural resourcesultimately declines, replacing it with tax revenues may require governments to give control of these proceeds tocitizens, in the form of cash transfers say, as a credible commitment to accountability, thereby breaking the countryout of its resource curse. |
| Keywords: | Tax Administration,Public Finance Decentralization and Poverty Reduction,Tax Law,Public Sector Economics,Services & Transfers to Poor,Access of Poor to Social Services,Disability,Economic Assistance,Economic Development,Macro-Fiscal Policy,Economic Adjustment and Lending,Taxation & Subsidies,Inequality |
| Date: | 2021–12–13 |
| URL: | http://d.repec.org/n?u=RePEc:wbk:wbrwps:9880&r= |
| By: | David Cerezo S\'anchez |
| Abstract: | Optimal simple rules for the monetary policy of the first stochastically dominant crypto-currency are derived in a Dynamic Stochastic General Equilibrium (DSGE) model, in order to provide optimal responses to changes in inflation, output, and other sources of uncertainty. The optimal monetary policy stochastically dominates all the previous crypto-currencies, thus the efficient portfolio is to go long on the stochastically dominant crypto-currency: a strategy-proof arbitrage featuring a higher Omega ratio with higher expected returns, inducing an investment-efficient Nash equilibrium over the crypto-market. Zero-knowledge proofs of the monetary policy are committed on the blockchain: an implementation is provided. |
| Date: | 2022–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2210.06139&r= |
| By: | Sanktjohanser, Anna |
| Abstract: | Models on reputational bargaining have introduced a perturbation with simple be-havioral types as a way of refining payo˙ predictions for the rational type. I show that this outcome refinement is not robust to the specification of the behavioral type. More specifically, I consider a slight relaxation of the strategy restriction on behavioral types relative to the literature, allowing behavioral types to choose their initial demands. I show that with this relaxation any feasible payo˙ can be achieved in equilibrium for the rational type when the probability of facing a behavioral type is small. My results highlight the implications of di˙erent perturbations for economic applications. |
| Date: | 2022–10–04 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:127402&r= |