nep-gth New Economics Papers
on Game Theory
Issue of 2021‒10‒11
fourteen papers chosen by
Sylvain Béal
Université de Franche-Comté

  1. Oddness of the number of Nash equilibria: the Case of Polynomial Payoff Functions By Philippe Bich; Julien Fixary
  2. Algorithmic aspects of core nonemptiness and core stability By Dylan Laplace Mermoud; Michel Grabisch; Peter Sudhölter
  3. On the empirical relevance of correlated equilibrium By Friedman, Dan; Rabanal, Jean Paul; Rud, Olga A; Zhao, Shuchen
  4. Bargaining theory over opportunity assignments and the egalitarian solution By Yongsheng Xu; Naoki Yoshihara
  5. Deep Learning for Principal-Agent Mean Field Games By Steven Campbell; Yichao Chen; Arvind Shrivats; Sebastian Jaimungal
  6. Information Design for a Non-atomic Service Scheduling Game By Nasimeh Heydaribeni; Ketan Savla
  7. Circles of Trust: Rival Information in Social Networks By Petra Persson ⓡ; Nikita Roketskiy ⓡ; Samuel Lee
  8. Standard vs random dictator games: On the effects of role uncertainty and framing on generosity By Ernesto Mesa-Vazquez; Ismael Rodriguez-Lara; Amparo Urbano
  9. The emergence of cooperation from shared goals in the Systemic Sustainability Game of common pool resources By Chengyi Tu; Paolo DOdorico; Zhe Li; Samir Suweis
  10. Cross-Examination By Claude Fluet; Thomas Lanzi
  11. Traders in a Strange Land: Agent-based discrete-event market simulation of the Figgie card game By Steven DiSilvio; Yu; Luo; Anthony Ozerov
  12. Feature Selection by a Mechanism Design By Xingwei Hu
  13. Coupled Fixed Points for Hardy-Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions By S. Kabaivanov; V. Zhelinski; B. Zlatanov
  14. Entry and exit decisions under public and private information: An experiment By Chernulich, Aleksei; Horowitz, John; Rabanal, Jean Paul; Rud, Olga A; Sharifova , Manizha

  1. By: Philippe Bich (Centre d'Economie de la Sorbonne, Paris School of Economics); Julien Fixary (Centre d'Economie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne)
    Abstract: In 1971, Robert Wilson ([19]) proved that "almost all" finite games have an odd number of mixed Nash equilibria (oddness theorem). Since then, several other proofs have been given, but always for mixed extensions of finite games. In this paper, we prove oddness theorem for large classes of polynomial payoff functions and semi-algebraic sets of strategies, and we provide some applications to recent models
    Keywords: Nash equilibria; polynomial payoff functions; generic oddness
    JEL: C02 C62 C72 D85
    Date: 2021–08
  2. By: Dylan Laplace Mermoud (Centre d'Economie de la Sorbonne); Michel Grabisch (Centre d'Economie de la Sorbonne); Peter Sudhölter (University of Southern Denmark, Department of Business and Economics)
    Abstract: In 1944, Von Neumann and Morgenstern developed the concept of stable sets as a solution for coalitional games. Fifteen years later, Gillies popularized the concept of the core, which is a convex polytope when nonempty. In the next decade, Bondareva and Shapley formulated independently a theorem describing a necessary and sufficient condition for the non emptiness of the core, using the mathematical objects of minimal balanced collections. We start our investigations of the core by implementing Peleg's (1965) inductive method for generating the minimal balanced collections as a computer program, and then, an algorithm that checks if a game admits a nonempty core or not. In 2020, Grabisch and Sudhölter formulated a theorem describing a necessary and sufficient condition for a game to admit a stable core, using several mathematical objects and concepts such as nested balancedness, balanced subsets which generalized balanced collections, exact and vital coalitions, etc. In order to reformulate the aforementioned theorem as an algorithm, a set of coalitions has to be found that, among other conditions, determines the core of the game. We study core stability, geometric properties of the core, and in particular, such core determining sets of coalitions. Furthermore, we describe a procedure for checking whether a subset of a given set is balanced. Finally, we implement the algorithm as a computer program that allows to check if an arbitrary balanced game admits a stable core or not
    Keywords: core; stable sets; balanced collections; core stability; cooperative game
    JEL: C71
    Date: 2021–07
  3. By: Friedman, Dan; Rabanal, Jean Paul (University of Stavanger); Rud, Olga A (University of Stavanger); Zhao, Shuchen
    Abstract: Can an efficient correlated equilibrium emerge without any exogenous benevolent agent providing coordinating signals? Theoretical work in adaptive dynamics suggests a positive answer, which we test in a laboratory experiment. In the well-known Chicken game, we observe time average play that is close to the asymmetric pure Nash equilibrium in some treatments, and in other treatments we observe collusive play. In a game resembling rock-paper-scissors or matching pennies, we observe time average play close to a correlated equilibrium that is more efficient than the unique Nash equilibrium. Estimates and simulations of adaptive dynamics capture much of the observed regularities.
    Keywords: Correlated equilibrium; Laboratory experiment; Adaptive dynamics
    JEL: A00
    Date: 2021–09–29
  4. By: Yongsheng Xu (Georgia State University,); Naoki Yoshihara (University of Massachusetts Amherst)
    Abstract: This paper discusses issues of axiomatic bargaining problems over opportunity assignments. The fair arbitrator uses the principle of 〠equal opportunity" for all players to make the recommendation on resource allocations. A framework in such a context is developed and the egalitarian solution to standard bargaining problems is reformulated and axiomatically characterized.
    Keywords: Opportunity sets, bargaining over opportunity assignments, egalitarian solution
    JEL: C71 C78 D60 D63 D70
    Date: 2021–09
  5. By: Steven Campbell; Yichao Chen; Arvind Shrivats; Sebastian Jaimungal
    Abstract: Here, we develop a deep learning algorithm for solving Principal-Agent (PA) mean field games with market-clearing conditions -- a class of problems that have thus far not been studied and one that poses difficulties for standard numerical methods. We use an actor-critic approach to optimization, where the agents form a Nash equilibria according to the principal's penalty function, and the principal evaluates the resulting equilibria. The inner problem's Nash equilibria is obtained using a variant of the deep backward stochastic differential equation (BSDE) method modified for McKean-Vlasov forward-backward SDEs that includes dependence on the distribution over both the forward and backward processes. The outer problem's loss is further approximated by a neural net by sampling over the space of penalty functions. We apply our approach to a stylized PA problem arising in Renewable Energy Certificate (REC) markets, where agents may rent clean energy production capacity, trade RECs, and expand their long-term capacity to navigate the market at maximum profit. Our numerical results illustrate the efficacy of the algorithm and lead to interesting insights into the nature of optimal PA interactions in the mean-field limit of these markets.
    Date: 2021–10
  6. By: Nasimeh Heydaribeni; Ketan Savla
    Abstract: We study an information design problem for a non-atomic service scheduling game. The service starts at a random time and there is a continuum of agent population who have a prior belief about the service start time but do not observe the actual realization of it. The agents want to make decisions of when to join the queue in order to avoid long waits in the queue or not to arrive earlier than the service has started. There is a planner who knows when the service starts and makes suggestions to the agents about when to join the queue through an obedient direct signaling strategy, in order to minimize the average social cost. We characterize the full information and the no information equilibria and we show in what conditions it is optimal for the planner to reveal the full information to the agents. Further, by imposing appropriate assumptions on the model, we formulate the information design problem as a generalized problem of moments (GPM) and use computational tools developed for such problems to solve the problem numerically.
    Date: 2021–09
  7. By: Petra Persson ⓡ; Nikita Roketskiy ⓡ; Samuel Lee
    Abstract: We analyze the diffusion of rival information in a social network. In our model, rational agents can share information sequentially, unconstrained by an exogenous protocol or timing. We show how to compute the set of eventually informed agents for any network, and show that it is essentially unique under altruistic preferences. The relationship between network structure and information diffusion is complex because the former shapes both the charity and confidentiality of potential senders and receivers.
    JEL: D83 D85
    Date: 2021–10
  8. By: Ernesto Mesa-Vazquez (Universidad de Valencia, ERICES); Ismael Rodriguez-Lara (Department of Economics, Universidad de Granada & Economic Science Institute (ESI), Chapman University); Amparo Urbano (Universidad de Valencia, ERICES)
    Abstract: We show that generosity is affected when we vary the level of role uncertainty, i.e., the probability that the dictator’s decision will be implemented. We also show that framing matters for generosity in that subjects are less generous when they are told that their choices will be implemented with a certain probability, compared with a setting in which they are told that their choices will not be implemented with certain probability.
    Keywords: dictator games, generosity, role uncertainty, framing effects
    JEL: C91 D3 D6 D81
    Date: 2021
  9. By: Chengyi Tu; Paolo DOdorico; Zhe Li; Samir Suweis
    Abstract: The sustainable use of common-pool resources (CPRs) is a major environmental governance challenge because of their possible over-exploitation. Research in this field has overlooked the feedback between user decisions and resource dynamics. Here we develop an online game to perform a set of experiments in which users of the same CPR decide on their individual harvesting rates, which in turn depend on the resource dynamics. We show that, if users share common goals, a high level of self-organized cooperation emerges, leading to long-term resource sustainability. Otherwise, selfish/individualistic behaviors lead to resource depletion ("Tragedy of the Commons"). To explain these results, we develop an analytical model of coupled resource-decision dynamics based on optimal control theory and show how this framework reproduces the empirical results.
    Date: 2021–10
  10. By: Claude Fluet; Thomas Lanzi
    Abstract: Two opposed parties seek to infl‡uence an uninformed decision maker. They invest in acquiring information and select what to disclose. The decision maker then adjudicates. We compare this benchmark with a procedure allowing adversarial cross-examination. A cross-examiner tests the opponent in order to persuade the decision maker that the opponent is deceitful. How does the opportunity or threat of cross-examination affect the parties' ’behavior? How does it affect the quality of decision-making? We show that decision-making deteriorates because parties are less likely to acquire information and because cross-examination too often makes the truth appear as falsehood. Next, we consider a form of controlled cross-examination by permitting the cross-examined to be re-examined by his own advocate, i.e., counter-persuasion. More information then reaches the decision maker. Decision-making may or may not improve compared to the benchmark depending on how examination is able to trade off type 1 and 2 errors.
    Keywords: : Bayesian persuasion, disclosure game, adversarial, redirect examination, procedural rules.
    JEL: C72 D71 D82 D83 K41
    Date: 2021
  11. By: Steven DiSilvio (Anna); Yu (Anna); Luo; Anthony Ozerov
    Abstract: Figgie is a card game that approximates open-outcry commodities trading. We design strategies for Figgie and study their performance and the resulting market behavior. To do this, we develop a flexible agent-based discrete-event market simulation in which agents operating under our strategies can play Figgie. Our simulation builds upon previous work by simulating latencies between agents and the market in a novel and efficient way. The fundamentalist strategy we develop takes advantage of Figgie's unique notion of asset value, and is, on average, the profit-maximizing strategy in all combinations of agent strategies tested. We develop a strategy, the "bottom-feeder", which estimates value by observing orders sent by other agents, and find that it limits the success of fundamentalists. We also find that chartist strategies implemented, including one from the literature, fail by going into feedback loops in the small Figgie market. We further develop a bootstrap method for statistically comparing strategies in a zero-sum game. Our results demonstrate the wide-ranging applicability of agent-based discrete-event simulations in studying markets.
    Date: 2021–10
  12. By: Xingwei Hu
    Abstract: In constructing an econometric or statistical model, we pick relevant features or variables from many candidates. A coalitional game is set up to study the selection problem where the players are the candidates and the payoff function is a performance measurement in all possible modeling scenarios. Thus, in theory, an irrelevant feature is equivalent to a dummy player in the game, which contributes nothing to all modeling situations. The hypothesis test of zero mean contribution is the rule to decide a feature is irrelevant or not. In our mechanism design, the end goal perfectly matches the expected model performance with the expected sum of individual marginal effects. Within a class of noninformative likelihood among all modeling opportunities, the matching equation results in a specific valuation for each feature. After estimating the valuation and its standard deviation, we drop any candidate feature if its valuation is not significantly different from zero. In the simulation studies, our new approach significantly outperforms several popular methods used in practice, and its accuracy is robust to the choice of the payoff function.
    Date: 2021–10
  13. By: S. Kabaivanov; V. Zhelinski; B. Zlatanov
    Abstract: In this paper we generalize Hardy-Rogers maps in the context of coupled fixed points. We generalizes with the help of the obtained main theorem some known results about existence and uniqueness of market equilibrium in duopoly markets. We investigate some recent results about market equilibrium in duopoly markets with the help of the main theorem and we enrich them. We define a generalized response function including production and surpluses. Finally we illustrate a possible application of the main result in the investigation of market equilibrium, when the pay off functions are non differentiable.
    Date: 2021–09
  14. By: Chernulich, Aleksei; Horowitz, John; Rabanal, Jean Paul (University of Stavanger); Rud, Olga A (University of Stavanger); Sharifova , Manizha
    Abstract: We design an experiment to study how reversible entry decisions are affected by public and private payoff disclosure policies. In our environment, subjects choose between a risky payoff, which evolves according to an autoregressive process, and a constant outside option payoff. The treatments vary the information disclosure rule on the risky payoff, such that in the public information treatment the risky payoff is always observable, while in the private information treatment, the risky payoff is observable only to the participants who enter the market. We find that under private information, market entry is higher, which suggests that subjects engage in exploration and place value on information.
    Keywords: experiment; entry and exit decisions; bandit problems; information pro- vision; forecasting
    JEL: C91 D81 D83 D84 G11
    Date: 2021–09–29

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