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on Game Theory |
| By: | Davide Carpentiere; Stephen Watson |
| Abstract: | We present a new proof for the existence of a Nash equilibrium, which involves no fixed point theorem. The self-contained proof consists of two parts. The first part introduces the notions of root function and pre-equilibrium. The second part shows the existence of pre-equilibria and Nash equilibria. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.01528&r=gth |
| By: | Daniele Condorelli; Massimiliano Furlan |
| Abstract: | We simulate behaviour of independent reinforcement learning algorithms playing the Crawford and Sobel (1982) game of strategic information transmission. We show that a sender and a receiver training together converge to strategies close to the exante optimal equilibrium of the game. Hence, communication takes place to the largest extent predicted by Nash equilibrium given the degree of conflict of interest between agents. The conclusion is shown to be robust to alternative specifications of the hyperparameters and of the game. We discuss implications for theories of equilibrium selection in information transmission games, for work on emerging communication among algorithms in computer science and for the economics of collusions in markets populated by artificially intelligent agents. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.07867&r=gth |
| By: | Dylan Possama\"i; Ludovic Tangpi |
| Abstract: | Commuters looking for the shortest path to their destinations, the security of networked computers, hedge funds trading on the same stocks, governments and populations acting to mitigate an epidemic, or employers and employees agreeing on a contact, are all examples of (dynamic) stochastic differential games. In essence, game theory deals with the analysis of strategic interactions among multiple decision-makers. The theory has had enormous impact in a wide variety of fields, but its rigorous mathematical analysis is rather recent. It started with the pioneering work of von Neumann and Morgenstern published in 1944. Since then, game theory has taken centre stage in applied mathematics and related areas. Game theory has also played an important role in unsuspected areas: for instance in military applications, when the analysis of guided interceptor missiles in the 1950s motivated the study of games evolving dynamically in time. Such games (when possibly subject to randomness) are called stochastic differential games. Their study started with the work of Issacs, who crucially recognised the importance of (stochastic) control theory in the area. Over the past few decades since Isaacs's work, a rich theory of stochastic differential game has emerged and branched into several directions. This paper will review recent advances in the study of solvability of stochastic differential games, with a focus on a purely probabilistic technique to approach the problem. Unsurprisingly, the number of players involved in the game is a major factor of the analysis. We will explain how the size of the population impacts the analyses and solvability of the problem, and discuss mean field games as well as the convergence of finite player games to mean field games. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.09919&r=gth |
| By: | Qianjun Lyu; Wing Suen |
| Abstract: | An uninformed sender publicly commits to an informative experiment about an uncertain state, privately observes its outcome, and sends a cheap-talk message to a receiver. We provide an algorithm valid for arbitrary state-dependent preferences that will determine the sender’s optimal experiment and his equilibrium payoff under binary state space. We give sufficient conditions for information design to be valuable or not under different payoff structures. These conditions depend more on marginal incentives - how payoffs vary with the state - than on the alignment of sender’s and receiver’s rankings over actions within a state. The algorithm can be easily modified to study canonical cheap talk games with a perfectly informed sender. |
| Keywords: | marginal incentives, common interest, concave envelope, quasiconcave envelope, double randomization |
| JEL: | D82 D83 |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2023_470&r=gth |
| By: | Zachary Feinstein; Niklas Hey; Birgit Rudloff |
| Abstract: | In Feinstein and Rudloff (2023), it was shown that the set of Nash equilibria for any non-cooperative $N$ player game coincides with the set of Pareto optimal points of a certain vector optimization problem with non-convex ordering cone. To avoid dealing with a non-convex ordering cone, an equivalent characterization of the set of Nash equilibria as the intersection of the Pareto optimal points of $N$ multi-objective problems (i.e.\ with the natural ordering cone) is proven. So far, algorithms to compute the exact set of Pareto optimal points of a multi-objective problem exist only for the class of linear problems, which reduces the possibility of finding the true set of Nash equilibria by those algorithms to linear games only. In this paper, we will consider the larger class of convex games. As, typically, only approximate solutions can be computed for convex vector optimization problems, we first show, in total analogy to the result above, that the set of $\epsilon$-approximate Nash equilibria can be characterized by the intersection of $\epsilon$-approximate Pareto optimal points for $N$ convex multi-objective problems. Then, we propose an algorithm based on results from vector optimization and convex projections that allows for the computation of a set that, on one hand, contains the set of all true Nash equilibria, and is, on the other hand, contained in the set of $\epsilon$-approximate Nash equilibria. In addition to the joint convexity of the cost function for each player, this algorithm works provided the players are restricted by either shared polyhedral constraints or independent convex constraints. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.04176&r=gth |
| By: | Dehez, Pierre (Université catholique de Louvain, LIDAM/CORE, Belgium) |
| Abstract: | We consider situations where players hit targets with known probabilities and are rewarded according to given rules. The division of the expected payoff resulting from their joint actions is studied in the context of transferable utility games, using the Shapley value as the allocation rule. |
| Keywords: | Probability games ; product games ; Shapley value |
| JEL: | C71 |
| Date: | 2023–05–31 |
| URL: | http://d.repec.org/n?u=RePEc:cor:louvco:2023017&r=gth |
| By: | Abheek Ghosh |
| Abstract: | We study the convergence of best-response dynamics in Tullock contests with convex cost functions (these games always have a unique pure-strategy Nash equilibrium). We show that best-response dynamics rapidly converges to the equilibrium for homogeneous agents. For two homogeneous agents, we show convergence to an $\epsilon$-approximate equilibrium in $\Theta(\log\log(1/\epsilon))$ steps. For $n \ge 3$ agents, the dynamics is not unique because at each step $n-1 \ge 2$ agents can make non-trivial moves. We consider the model proposed by \cite{ghosh2023best}, where the agent making the move is randomly selected at each time step. We show convergence to an $\epsilon$-approximate equilibrium in $O(\beta \log(n/(\epsilon\delta)))$ steps with probability $1-\delta$, where $\beta$ is a parameter of the agent selection process, e.g., $\beta = n^2 \log(n)$ if agents are selected uniformly at random at each time step. We complement this result with a lower bound of $\Omega(n + \log(1/\epsilon)/\log(n))$ applicable for any agent selection process. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.03528&r=gth |
| By: | Ashkenazi-Golan, Galit; Hernández, Penélope; Neeman, Zvika; Solan, Eilon |
| Abstract: | This paper addresses the question of how to best communicate information over time in order to influence an agent's belief and induced actions in a model with a binary state of the world that evolves according to a Markov process, and with a finite number of actions. We characterize the sender's optimal message strategy in the limit, as the length of each period decreases to zero. We show that the limit optimal strategy is myopic for beliefs smaller than the invariant distribution of the underlying Markov process. For beliefs larger than the invariant distribution, the optimal policy is more elaborate and involves both silence and splitting of the receiver's beliefs; it is not myopic. |
| Keywords: | Bayesian persuasion; information design; Markov games; repeated games with incomplete information; 2510/17; Elsevier deal |
| JEL: | D82 D83 |
| Date: | 2023–11–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:119970&r=gth |
| By: | Giorgio Fabbri (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, CNRS - Centre National de la Recherche Scientifique); Salvatore Federico (UniGe - Università degli studi di Genova = University of Genoa); Davide Fiaschi (University of Pisa - Università di Pisa); Fausto Gozzi (LUISS - Libera Università Internazionale degli Studi Sociali Guido Carli [Roma]) |
| Abstract: | We propose a model, which nests a susceptible-infected-recovered-deceased (SIRD) epidemic model into a dynamic macroeconomic equilibrium framework with agents' mobility. The latter affect both their income and their probability of infecting and being infected. Strategic complementarities among individual mobility choices drive the evolution of aggregate economic activity, while infection externalities caused by individual mobility affect disease diffusion. The continuum of rational forward-looking agents coordinates on the Nash equilibrium of a discrete time, finite-state, infinite-horizon Mean Field Game. We prove the existence of an equilibrium and provide a recursive construction method for the search of an equilibrium(a), which also guides our numerical investigations. We calibrate the model by using Italian experience on COVID-19 epidemic and we discuss policy implications. |
| Keywords: | Mean field game, Strategic complementarities, ESIRD, COVID-19 |
| Date: | 2023–02–24 |
| URL: | http://d.repec.org/n?u=RePEc:hal:journl:hal-04153998&r=gth |
| By: | Davide Fiaschi; Cristiano Ricci |
| Abstract: | This paper studies the spatial agglomeration of workers and income in a continuous space and time framework. Production and consumption are decided in local markets, characterized by the presence of spatial spillovers and amenities. Workers move across locations maximizing their instantaneous utility, subject to mobility costs. We prove the existence of a short-run Cournot-Nash equilibrium, and that, in the limit of an infinite number of workers, the sequence of short-run equilibria can be expressed by a partial differential equation. We characterize the conditions under which the long-run equilibrium displays spatial agglomerations. Social welfare is non-decreasing over time, and in the long-run equilibrium the expected utility of a representative worker is equalized over space and, therefore, the spatial allocation is efficient. The model can reproduce several stylized effects, such as the emergence of spatial agglomerations (cities) with different sizes and shapes; the dependence by history of spatial pattern of economic activities; a non-linear out-of-equilibrium dynamics; and finally, the phenomenon of metastability, where a long period of apparent stability in the spatial distribution is followed by a sharp transition to a new equilibrium. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.07883&r=gth |
| By: | Junichiro Ishida; Wing Suen |
| Abstract: | We introduce behavioral diversity to an otherwise standard signaling model, in which a fraction of agents choose their signaling actions according to an exogenous distribution. These behavioral agents provide opportunities for strategic low-type agents to successfully emulate higher types in equilibrium, which in turn reduces the cost for strategic high-type agents to separate from lower types. Behavioral diversity thus improves the equilibrium payoffs to all types of strategic agents. The model also exhibits a convergence property which is intuitively more appealing than the least-cost separating equilibrium of the standard setting. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:dpr:wpaper:1216&r=gth |
| By: | Dirk Bergemann (Yale University); Tan Gan (Yale University); Yingkai Li (Yale University) |
| Abstract: | We study a sender-receiver model where the receiver can commit to a decision rule before the sender determines the information policy. The decision rule can depend on the signal structure and the signal realization that the sender adopts. This framework captures applications where a decision-maker (the receiver) solicit advice from an interested party (sender). In these applications, the receiver faces uncertainty regarding the senderÕs preferences and the set of feasible signal structures. Consequently, we adopt a unified robust analysis framework that includes max-min utility, min-max regret, and min-max approximation ratio as special cases. We show that it is optimal for the receiver to sacrifice ex-post optimality to perfectly align the senderÕs incentive. The optimal decision rule is a quota rule, i.e., the decision rule maximizes the receiverÕs ex-ante payoff subject to the constraint that the marginal distribution over actions adheres to a consistent quota, regardless of the senderÕs chosen signal structure. |
| Date: | 2023–10–19 |
| URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:2372&r=gth |
| By: | Nisvan Erkal (Department of Economics, University of Melbourne); Boon Han Koh (Department of Economics, University of Exeter); Nguyen Lam (Department of Economics, University of Melbourne) |
| Abstract: | Many economic activities rely on teamwork where groups of individuals work together for a common goal by pooling their resources or skills. However, cooperation within teams can be challenging due to the social dilemma problem which arises when individual incentives interfere with operational effectiveness. We study teamwork in a dynamic public goods game setting where individuals make multiple contribution decisions to a team project and face strategic uncertainty about the behavior of their team members. We examine whether providing feedback about the team’s progress at regular intervals (time-based feedback) or based on the achievement of milestones (milestone-based feedback) is more beneficial for increasing aggregate contributions. Our results reveal that providing milestone-based feedback leads to a significant increase in aggregate team contributions as compared to time-based feedback. This impact is largely driven by conditional cooperators. Findings from a follow-up experiment reveal evidence of a goal effect, a signaling effect, and an information effect arising from the use of milestones on the behavior of conditional cooperators. |
| Keywords: | teamwork, public good provision, milestones, feedback, voluntary contribution mechanism |
| JEL: | C92 D83 D91 H41 |
| Date: | 2023–09–12 |
| URL: | http://d.repec.org/n?u=RePEc:exe:wpaper:2310&r=gth |
| By: | Valsecchi, Irene |
| Abstract: | For two periods an expert E announces his forecast of the state to a decision-maker D who chooses action. They disagree about the precision of the probability assessments. At the end of period 1 the state is observed. In the last period E makes announcements more extreme than his forecasts. Despite countable equilibria, full revelation is never realised. When in period 1 E is interested in reputation only, the initial equilibrium partition is finite; E makes announcements of greater uncertainty with respect to his forecasts. When E is interested in action too, reputational concerns mitigate exaggerated reports. |
| Keywords: | Research Methods/ Statistical Methods |
| Date: | 2023–10–26 |
| URL: | http://d.repec.org/n?u=RePEc:ags:feemwp:338779&r=gth |
| By: | Thomas Falconer; Jalal Kazempour; Pierre Pinson |
| Abstract: | Reliably forecasting uncertain power production is beneficial for the social welfare of electricity markets by reducing the need for balancing resources. Describing such forecasting as an analytics task, the current literature proposes analytics markets as an incentive for data sharing to improve accuracy, for instance by leveraging spatio-temporal correlations. The challenge is that, when used as input features for forecasting, correlated data complicates the market design with respect to the revenue allocation, as the value of overlapping information is inherently combinatorial. We develop a correlation-aware analytics market for a wind power forecasting application. To allocate revenue, we adopt a Shapley value-based attribution policy, framing the features of agents as players and their interactions as a characteristic function game. We illustrate that there are multiple options to describe such a game, each having causal nuances that influence market behavior when features are correlated. We argue that no option is correct in a general sense, but that the decision hinges on whether the market should address correlations from a data-centric or model-centric perspective, a choice that can yield counter-intuitive allocations if not considered carefully by the market designer. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.06000&r=gth |
| By: | Azam, Jean-Paul |
| Abstract: | This paper presents an interpretation of the main arguments used in Peter Olivi’s Treatise on Demons, published circa 1295 in Narbonne, Languedoc, within a rational-choice framework. This book has been widely praised as a landmark in the philosophical literature on personhood and personal freedom, since it was (re)discovered about a century ago. In it, Olivi discusses most of the relevant classical and medieval literature on this topic before stating his own position. In the scholastic tradition, the book does not make for easy reading. Moreover, it is evidently a “work in progress”, as pointed out by the translator. Many paragraphs end with “Ergo, etc.”, suggesting that he planned to add something, but could not find time enough for that. He died in 1298, aged 50. This paper offers a simple game-theoretic model aimed at articulating Olivi’s main arguments in a consistent rational choice framework, supported by many quotes translated from French into English by me. It suggests that the “fall of the devil” is used as a parable on human freedom and agency, given a set of incentives strategically chosen by “God” to minimize the number of “sinners”, with some potential interference by “Lucifer”. |
| JEL: | B11 B30 P48 Z12 |
| Date: | 2023–10–26 |
| URL: | http://d.repec.org/n?u=RePEc:tse:wpaper:128653&r=gth |
| By: | Olivier Compte |
| Abstract: | We propose a belief-formation model where agents attempt to discriminate between two theories, and where the asymmetry in strength between confirming and disconfirming evidence tilts beliefs in favor of theories that generate strong (and possibly rare) confirming evidence and weak (and frequent) disconfirming evidence. In our model, limitations on information processing provide incentives to censor weak evidence, with the consequence that for some discrimination problems, evidence may become mostly one-sided, independently of the true underlying theory. Sophisticated agents who know the characteristics of the censored data-generating process are not lured by this accumulation of ``evidence'', but less sophisticated ones end up with biased beliefs. |
| Date: | 2023–10 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:2310.08466&r=gth |