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on Game Theory |
| By: | Zola, Maurizio |
| Abstract: | In a previous paper [1] the application of the dominance principle was proposed to find the non-cooperative solution of two persons two by two general sum game with mixed strategies; in this way it was possible to choose the equilibrium point among the classical solutions avoiding the ambiguity due to their non-interchangeability, moreover the non-cooperative equilibrium point was determined by a new approach based on the dominance principle [2]. Starting from that result it is here below proposed the extension of the method to more than two persons general sum games with n by n moves. Generally speaking the dominance principle can be applied to fi nd the equilibrium point both in pure and mixed strategies. In this paper in order to apply the dominance principle to the mixed strategies solution, the algebraic multi-linear forms of the expected payoffs of the players are studied. From these expressions of the expected payoffs the derivatives are obtained and they are used to express the probabilities distribution on the moves after the two defi nitions as Nash and prudential strategies [1]. The application of the dominance principle allows to choose the equilibrium point between the two equivalent solutions avoiding the ambiguity due to their non-interchangeability and a conjecture about the uniqueness of the solution is proposed in order to solve the problem of the existence and uniqueness of the non-cooperative solution of a many persons n by n game. The uniqueness of the non-cooperative solution could be used as a starting point to find out the cooperative solution of the game too. Some games from the sound literature are discussed in order to show the effectiveness of the presented procedure. |
| Keywords: | Dominance principle; General sum game; pure strategy, mixed strategy. |
| JEL: | C72 |
| Date: | 2024–10–18 |
| URL: | https://d.repec.org/n?u=RePEc:pra:mprapa:122448 |
| By: | Jian-Qiao Zhu; Joshua C. Peterson; Benjamin Enke; Thomas L. Griffiths |
| Abstract: | Understanding how people behave in strategic settings–where they make decisions based on their expectations about the behavior of others–is a longstanding problem in the behavioral sciences. We conduct the largest study to date of strategic decision-making in the context of initial play in two-player matrix games, analyzing over 90, 000 human decisions across more than 2, 400 procedurally generated games that span a much wider space than previous datasets. We show that a deep neural network trained on these data predicts people’s choices better than leading theories of strategic behavior, indicating that there is systematic variation that is not explained by those theories. We then modify the network to produce a new, interpretable behavioural model, revealing what the original network learned about people: their ability to optimally respond and their capacity to reason about others are dependent on the complexity of individual games. This context-dependence is critical in explaining deviations from the rational Nash equilibrium, response times, and uncertainty in strategic decisions. More broadly, our results demonstrate how machine learning can be applied beyond prediction to further help generate novel explanations of complex human behavior. |
| Keywords: | behavioural game theory, large scale experiment, machine learning, behavioral economics, complexity |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:ces:ceswps:_11296 |
| By: | Zhengyang Liu; Haolin Lu; Liang Shan; Zihe Wang |
| Abstract: | In this paper, we consider the dynamic oscillation in the Cournot oligopoly model, which involves multiple firms producing homogeneous products. To explore the oscillation under the updates of best response strategies, we focus on the linear price functions. In this setting, we establish the existence of oscillations. In particular, we show that for the scenario of different costs among firms, the best response converges to either a unique equilibrium or a two-period oscillation. We further characterize the oscillations and propose linear-time algorithms for finding all types of two-period oscillations. To the best of our knowledge, our work is the first step toward fully analyzing the periodic oscillation in the Cournot oligopoly model. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.09435 |
| By: | Yuma Fujimoto; Kaito Ariu; Kenshi Abe |
| Abstract: | Auction is one of the most representative buying-selling systems. A celebrated study shows that the seller's expected revenue is equal in equilibrium, regardless of the type of auction, typically first-price and second-price auctions. Here, however, we hypothesize that when some auction environments vary with time, this revenue equivalence may not be maintained. In second-price auctions, the equilibrium strategy is robustly feasible. Conversely, in first-price auctions, the buyers must continue to adapt their strategies according to the environment of the auction. Surprisingly, we prove that revenue equivalence can be broken in both directions. First-price auctions bring larger or smaller revenue than second-price auctions, case by case, depending on how the value of an item varies. Our experiments also demonstrate revenue inequivalence in various scenarios, where the value varies periodically or randomly. This study uncovers a phenomenon, the breaking of revenue equivalence by the time-varyingness in auctions, that likely occurs in real-world auctions, revealing its underlying mechanism. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.12306 |
| By: | Guerrazzi, Marco |
| Abstract: | In this paper, I explore the relationship between wage bargaining and capital accumulation by developing a differential game in which a monopolistic union sets the wage of its members by taking as given the optimal employment strategy of a representative firm and the way in which capital is evaluated over time. Under the assumption that investment amounts to a constant share of produced output, I show that a meaningful open-loop Stackelberg equilibrium requires the union to be more patient than the firm. Moreover, relying on some numerical simulations, I show that although adjustments towards the steady-state equilibrium occur through damped oscillations, after an initial period of decline, the model predicts a stable union wage premium. |
| Keywords: | Monopoly union model, Capital accumulation, Binding wage contracts, Differential games, Open-loop Stackelberg equilibrium |
| JEL: | J31 J51 J52 |
| Date: | 2024 |
| URL: | https://d.repec.org/n?u=RePEc:zbw:glodps:1515 |
| By: | Dehez, Pierre (Université catholique de Louvain, LIDAM/CORE, Belgium); Ferey, Samuel (University of Lorraine) |
| Abstract: | Leniency programs in antitrust investigations exist in Europe since the late nineties. They cover secret agreements and concerted practices between companies, and provide total or partial immunity to companies reporting evidence. This raises the question of assessing correctly the contribution of each company that take part in a leniency program. This question is formalized within a cooperative game with transferable utility. The resulting game being convex, its core is nonempty and contains the Shapley value in its center. It defines a reference allocation that treats the participants symmetrically. In practice, companies report sequentially leading to allocations that are vertices of the core. |
| Keywords: | Competition law ; leniency programs ; core ; Shapley value |
| JEL: | L40 K21 C71 |
| Date: | 2024–05–13 |
| URL: | https://d.repec.org/n?u=RePEc:cor:louvco:2024008 |
| By: | Dirk Bergemann (Yale University); Stephen Morris (Massachusetts Institute of Technology); Rafael Veiel (Massachusetts Institute of Technology) |
| Abstract: | Two information structures are said to be close if, with high probability, there is approximate common knowledge that interim beliefs are close under the two information structures. We define an Òalmost common knowledge topologyÓ reflecting this notion of closeness. We show that it is the coarsest topology generating continuity of equilibrium outcomes. An information structure is said to be simple if each player has a finite set of types and each type has a distinct first-order belief about payoff states. We show that simple information structures are dense in the almost common knowledge topology and thus it is without loss to restrict attention to simple information structures in information design problems. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:cwl:cwldpp:2413 |
| By: | Pranjal Rawat |
| Abstract: | Traditional methods for computing equilibria in auctions become computationally intractable as auction complexity increases, particularly in multi-item and dynamic auctions. This paper introduces a self-play based reinforcement learning approach that employs advanced algorithms such as Proximal Policy Optimization and Neural Fictitious Self-Play to approximate Bayes-Nash equilibria. This framework allows for continuous action spaces, high-dimensional information states, and delayed payoffs. Through self-play, these algorithms can learn robust and near-optimal bidding strategies in auctions with known equilibria, including those with symmetric and asymmetric valuations, private and interdependent values, and multi-round auctions. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.13960 |
| By: | Ryoji Jinushi |
| Abstract: | As consumers have limited capacity to process information, advertisers must compete for attention. This creates information congestion which produces social loss like unread advertisements. We apply population games and best response dynamics to analyze information congestion. Multiple equilibria impair traditional policies, and thus, non-traditional policies are examined to lead the system to a Pareto efficient equilibrium. We achieve this by changing the cost per message multiple times during the evolutionary process. In this process, policymakers gradually but incompletely investigate externalities and adjust the speed of cost changes. Such complicated policies are costly, which confirms the inefficiency of advertising structures where advertisers send unsolicited messages. |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:tcr:wpaper:e210 |
| By: | Brendan Kline; Elie Tamer |
| Abstract: | We address counterfactual analysis in empirical models of games with partially identified parameters, and multiple equilibria and/or randomized strategies, by constructing and analyzing the counterfactual predictive distribution set (CPDS). This framework accommodates various outcomes of interest, including behavioral and welfare outcomes. It allows a variety of changes to the environment to generate the counterfactual, including modifications of the utility functions, the distribution of utility determinants, the number of decision makers, and the solution concept. We use a Bayesian approach to summarize statistical uncertainty. We establish conditions under which the population CPDS is sharp from the point of view of identification. We also establish conditions under which the posterior CPDS is consistent if the posterior distribution for the underlying model parameter is consistent. Consequently, our results can be employed to conduct counterfactual analysis after a preliminary step of identifying and estimating the underlying model parameter based on the existing literature. Our consistency results involve the development of a new general theory for Bayesian consistency of posterior distributions for mappings of sets. Although we primarily focus on a model of a strategic game, our approach is applicable to other structural models with similar features. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.12731 |
| By: | Neil A. Chriss |
| Abstract: | This is the third paper in a series concerning the game-theoretic aspects of position-building while in competition. The first paper set forth foundations and laid out the essential goal, which is to minimize implementation costs in light of how other traders are likely to trade. The majority of results in that paper center on the two traders in competition and equilibrium results are presented. The second paper, introduces computational methods based on Fourier Series which allows the introduction of a broad range of constraints into the optimal strategies derived. The current paper returns to the unconstrained case and provides a complete solution to finding equilibrium strategies in competition and handles completely arbitrary situations. As a result we present a detailed analysis of the value (or not) of trade centralization and we show that firms who naively centralize trades do not generally benefit and sometimes, in fact, lose. On the other hand, firms that strategically centralize their trades generally will be able to benefit. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.13583 |
| By: | Takashi Furuya; Anastasis Kratsios |
| Abstract: | Forward-backwards stochastic differential equations (FBSDEs) are central in optimal control, game theory, economics, and mathematical finance. Unfortunately, the available FBSDE solvers operate on \textit{individual} FBSDEs, meaning that they cannot provide a computationally feasible strategy for solving large families of FBSDEs as these solvers must be re-run several times. \textit{Neural operators} (NOs) offer an alternative approach for \textit{simultaneously solving} large families of FBSDEs by directly approximating the solution operator mapping \textit{inputs:} terminal conditions and dynamics of the backwards process to \textit{outputs:} solutions to the associated FBSDE. Though universal approximation theorems (UATs) guarantee the existence of such NOs, these NOs are unrealistically large. We confirm that ``small'' NOs can uniformly approximate the solution operator to structured families of FBSDEs with random terminal time, uniformly on suitable compact sets determined by Sobolev norms, to any prescribed error $\varepsilon>0$ using a depth of $\mathcal{O}(\log(1/\varepsilon))$, a width of $\mathcal{O}(1)$, and a sub-linear rank; i.e. $\mathcal{O}(1/\varepsilon^r)$ for some $r |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.14788 |
| By: | Masaki Aoyagi (ISER, Osaka University); Maxime Menuet (Université Côte d'Azur, CNRS, GREDEG, France) |
| Abstract: | This paper studies the optimal disclosure of information about an agent's quality when it is a combination of a component privately observed by the agent and another latent component. Upon soliciting a report from the agent about his private observation, a principal performs a test which reveals the latent component. The principal then discloses information to the market/public which rewards the agent with compensation equal to the agent's expected quality. We study incentive compatible disclosure rules that minimize the mismatch between the agent's true and expected qualities while inducing truth-telling from the agent. The optimal rule entails full disclosure when the agent's quality is a supermodular function of the two components, but entails partial pooling when it is submodular. We express the optimization problem as a linear transformation of the mean dual-belief, which describes the joint distribution of prior and mean posterior beliefs under disclosure, and obtain the optimal disclosure rule as a corner solution to this linear problem. We identify the number of messages required under the optimal rule and relate it to the agent's incentive compatibility conditions. |
| Keywords: | quality, mechanism, revelation, pooling, separating |
| JEL: | C72 D47 D82 |
| Date: | 2024–11 |
| URL: | https://d.repec.org/n?u=RePEc:gre:wpaper:2024-30 |
| By: | Lefebvre, Mathieu (University of Strasbourg); Pestieau, Pierre (Université catholique de Louvain, LIDAM/CORE, Belgium); Schoenmaeckers, Jérôme (Université de Liège) |
| Abstract: | The phenomenon of grandparents assuming the role of caretakers for their grandchildren is both substantial and on the rise, a trend partially attributed to mothers’ increasing participation in the workforce. While altruism is commonly believed to be the primary driver behind such caregiving, we propose to examine an additional motivation: the expectation among grandparents that they will receive care from their offspring in the event of their own incapacity. This paper aims to investigate this hypothesis from both theoretical and empirical perspectives. Initially, we construct a theoretical framework, delineating a Subgame Perfect Nash Equilibrium, wherein the grandparent first commits to caring for the grandchild, followed by the anticipation of receiving care from their adult child in scenarios of disability. Subsequently, we empirically test the feasibility of this model by analyzing data sourced from the Survey of Health, Ageing and Retirement in Europe (SHARE). Our results confirm that elderly who took care of their grandchildren receive more support from their children in the case of a loss of autonomy. |
| Keywords: | Long-term care ; Intergenerational transfers ; Informal care |
| JEL: | D13 J14 D64 |
| Date: | 2024–05–30 |
| URL: | https://d.repec.org/n?u=RePEc:cor:louvco:2024014 |
| By: | Kento Yoshida; Kei Kimura; Taiki Todo; Makoto Yokoo |
| Abstract: | Facility location games provide an abstract model of mechanism design. In such games, a mechanism takes a profile of $n$ single-peaked preferences over an interval as an input and determines the location of a facility on the interval. In this paper, we restrict our attention to distance-based single-peaked preferences and focus on a well-known class of parameterized mechanisms called ordered weighted average methods, which is proposed by Yager in 1988 and contains several practical implementations such as the standard average and the Olympic average. We comprehensively analyze their performance in terms of both incentives and fairness. More specifically, we provide necessary and sufficient conditions on their parameters to achieve strategy-proofness, non-obvious manipulability, individual fair share, and proportional fairness, respectively. |
| Date: | 2024–10 |
| URL: | https://d.repec.org/n?u=RePEc:arx:papers:2410.12884 |
| By: | Ornella Tarola (DISSE, University of Rome La Sapienza, Rome, Italy); Emmanuelle Taugourdeau (CNRS, CREST, Palaiseau, France) |
| Abstract: | In light of the ongoing debate on Common But Differentiated Responsibilities (CBDR), we wonder whether it is worthwile for industrialized countries to take the lead in reducing emissions, rather than acting simultaneously with less advanced countries. To do this, we compare national payoffs and global emissions in each situation. We also examine whether industrial leakage is an inevitable outcome of asymmetric policies with differentiated abatement responsibilities and, if so, whether unambigously hurts the more industrialized countries. We show that leadership can improve payoffs while reducing global emissions, even though these goals appear to be at odds. |
| Keywords: | Tax Competition, Capital Integration, Global Pollution, Environmental agreements |
| JEL: | H2 R3 R5 Q5 |
| Date: | 2024–11–01 |
| URL: | https://d.repec.org/n?u=RePEc:crs:wpaper:2024-11 |