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on Game Theory |
| By: | Heifetz, Aviad; Peña, Jorge |
| Abstract: | In the standard continuous-time choice-taking gradient dynamics in smooth two-player games, each player implicitly assumes that their opponent momentarily main-tains their last choice. Contrastingly, in the utility-taking gradient dynamics each player implicitly assumes that their opponent momentarily maintains their utility level, by marginally adjusting their choice to that effect. Somewhat surprisingly, employing a transversality argument we find that, in an open and dense set of smooth games, this dynamics is undefined at Nash equilibria. This occurs because, at a Nash equilibrium, the opponent’s indifference curve is not locally a function of one’s own strategy, mak-ing it impossible to specify an opponent’s adjustment that would maintain their utility in response to one’s own marginal deviation from Nash behavior. Furthermore, when approaching a Nash equilibrium of such a generic game, the utility-taking gradient dy-namics either accelerates without bound towards the equilibrium or diverges away from it with unbounded speed. |
| Keywords: | gradient dynamics |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:tse:wpaper:130433 |
| By: | Srihari Govindan (Department of Economics, University of Rochester, Rochester, USA); Rida Laraki (Morrocan Center for Game Theory, UM6P, Rabat, Morocco); Lucas Pahl (School of Economics, University of Sheffield, Sheffield S1 4DT, UK) |
| Abstract: | We present the following analog of O’Neill’s Theorem (Theorem 5.2 in [17]) for finite games. Let C1, . . . , Ck be the components of Nash equilibria of a finite normal-form game G. For each i, let ci be the index of Ci. For each ε > 0, there exist pairwise disjoint neighborhoods V1, ..., Vk of the components such that for any choice of finitely many distinct completely mixed strategy profiles {σij}ij, σij ∈ Vi for each i = 1, . . . , k and numbers rij ∈ {−1, 1} such that j rij = ci, there exists a normal-form game G¯ obtained from G by adding duplicate strategies and an ε-perturbation G¯ε of G¯ such that the set of equilibria of G¯ε is {σ¯ij}ij , where for each i, j:(1) σ¯ij is equivalent to the profile σij; (2) the index σ¯ij equals rij. |
| Keywords: | Game Theory, Index Theory, Fixed Point Theory |
| JEL: | C72 |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:shf:wpaper:2025002 |
| By: | Lucas Pahl (School of Economics, University of Sheffield, Sheffield S1 4DT, UK); Carlos Pimienta (School Of Economics, The University of New South Wales, Sydney, Australia) |
| Abstract: | We prove the 2-player, generic extensive-form case of the conjecture of Govindan and Wilson (1997a, b) and Hauk and Hurkens (2002) stating that an equilibrium component is essential in every equivalent game if and only if the index of the component is nonzero. This provides an index-theoretic characterization of the concept of hyperstable components of equilibria in generic extensive-form games, first formulated by Kohlberg and Mertens (1986). We also illustrate how to compute hyperstable equilibria in multiple economically relevant examples and show how the predictions of hyperstability compare with other solution concepts. |
| Keywords: | Game Theory, Robustness of Equilibria, Fixed Point Theory, Index Theory |
| JEL: | C72 |
| Date: | 2025–01 |
| URL: | https://d.repec.org/n?u=RePEc:shf:wpaper:2025001 |
| By: | Heijmans, Roweno J.R.K. (Dept. of Business and Management Science, Norwegian School of Economics); Suetens, Sigrid (Dept. of Economics, CentER, Tilburg University) |
| Abstract: | We use experiments to systematically test the performance of subsidies aimed at inducing efficient coordination in a coordination game. We consider two classes of policies: those based on divide-and-conquer (i.e. iterated dominance) and those making the efficient Nash equilibrium of the game risk dominant. Cost-efficient policies from both classes are equally expensive but differ in the distribution of subsidies among agents. Our results show that risk dominance subsidies increase coordination more effectively or at a lower cost than divide-and-conquer subsidies. |
| Keywords: | Coordination; policy design; divide-and-conquer; risk dominance; experiment; contracting with externalities |
| JEL: | C70 C90 D04 H20 |
| Date: | 2025–03–07 |
| URL: | https://d.repec.org/n?u=RePEc:hhs:nhhfms:2025_009 |
| By: | Andreas Hefti; Peiyao Shen |
| Abstract: | Understanding disparities in contest success is central to explaining how competition shapes the distribution of rewards, influence, or market shares. We introduce the Proportional Play Equilibrium (PPE), a boundedly rational alternative to Nash Equilibrium (NE) grounded in the Illusion of Proportionality, and show that it results in more unequal outcomes by exaggerating the success chances of stronger contestants. Laboratory evidence strongly supports PPE’s predictions for success dispersion while rejecting those of NE. Our results highlight how equilibrium analysis under full rationality may mischaracterize the inequality-generating effects of competition, with further implications for understanding inequality in markets or political contests. |
| Keywords: | Illusion of proportionality, bounded rationality, contest success, market share and inequality, behavioral contest theory |
| JEL: | D01 D91 D72 C72 |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:zur:econwp:466 |
| By: | Dietzenbacher, Bas (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory); Vermeulen, Dries (RS: GSBE other - not theme-related research, QE Math. Economics & Game Theory, RS: GSBE MCM) |
| Abstract: | For communication situations where the communication possibilities of players are modeled by an undirected graph, we study to what extent Myerson’s graph-restricted game inherits properties from the original transferable utility game. We focus on monotonicity, additivity, superadditivity, convexity, imputation admissibility, balancedness, total balancedness, population monotonic allocation schemes, and exactness. For each of these properties, we characterize all communication graphs that guarantee the inheritance. We present existing results from the literature and we provide new results. |
| JEL: | C71 |
| Date: | 2025–03–31 |
| URL: | https://d.repec.org/n?u=RePEc:unm:umagsb:2025003 |
| By: | Christian Ewerhart |
| Abstract: | This paper examines the definition and continuity of expected payoffs in compact games with continuous payoff functions. There are three main results. First, we confirm that Glicksberg’s (1952) original definition of expected payoffs as an iterated integral is mathematically sound under general conditions. Second, we show that the now more common definition as a single integral is both rigorous and equivalent to the original when strategy spaces are either Hausdorff or second countable. Third, we offer an alternative proof of the continuity of expected payoffs without imposing the Hausdorff separation axiom. Together, these results lead to a strengthening of Glicksberg’s theorem on equilibrium existence in compact Hausdorff games with continuous payoff functions. |
| Keywords: | Compact games, expected payoffs, weak* topology, measurability, continuity |
| JEL: | C72 |
| Date: | 2025–03 |
| URL: | https://d.repec.org/n?u=RePEc:zur:econwp:467 |
| By: | Moav, Omer (University of Warwick & Reichman University); Pascali, Luigi (UPF & LUISS); Pauzner, Ady (Tel Aviv University & Reichman University) |
| Abstract: | Cooperation in joint ventures is widespread, despite its vulnerability to defection. It can emerge when the interaction is repeated and agents are patient enough to prefer the benefits of future cooperation over the short-term gains from defection. Thus, if a large fraction of the population consists of impatient exploiters who always defect and agents are randomly paired to play a repeated prisoner dilemma game, patient agents defect as well, and society is in a no-cooperation trap. We show that the existence of an outside option can break this trap even if the fraction of patient agents is arbitrarily small. Impatient agents self-select out of the game, allowing patient agents to cooperate. Patience thus has an evolutionary advantage, leading to widespread cooperation. |
| Date: | 2025 |
| URL: | https://d.repec.org/n?u=RePEc:wrk:warwec:1554 |
| By: | Christian Ewerhart |
| Abstract: | This paper identifies a central role of the topological separation axiom T1 in the definition of mixed strategies in noncooperative games with arbitrary pure strategy spaces. Our main result says that a pure strategy space is topologically T1 if and only if (i) all singleton strategy sets are Borel, (ii) all Dirac measures are regular, and (iii) the canonical mapping from pure strategies to Dirac measures is one-to-one. The analysis therefore suggests that the T1 separation axiom is a minimum requirement on the topology of a pure strategy space when randomization is allowed for. Using an example, we show that the T1 assumption is indeed missing from the minimax theorem of Mertens (1986). |
| Keywords: | Mixed strategies, Hausdorff spaces, T1 separation axiom, minimax theorem |
| JEL: | C72 |
| Date: | 2025–04 |
| URL: | https://d.repec.org/n?u=RePEc:zur:econwp:468 |
| By: | Dongkyu Chang (City University of Hong Kong); Duk Gyoo Kim (Yonsei University); Wooyoung Lim (Hong Kong University of Science and Technology) |
| Abstract: | In dynamic screening problems between an uninformed seller and a privately-informed buyer, theory suggests that the presence of the buyer’s outside option leads to a significant surplus for the seller. However, this prediction relies on multiple layers of positive selection reasoning. To examine whether participants demonstrate positive selection in their belief updates, we conduct a two-round bargaining experiment with finite price alternatives, which enable us to identify first-, second-, and third-order positive selection reasoning. Few subjects adhere to the equilibrium reasoning, and the majority fail even at the first-order reasoning. Consequently, the seller payoffs fall short of the theoretical benchmark. |
| Keywords: | Positive Selection, Outside Options, Laboratory Experiments |
| JEL: | C78 C91 D03 |
| Date: | 2025–02 |
| URL: | https://d.repec.org/n?u=RePEc:yon:wpaper:2025rwp-238 |
| By: | Igor Sadoune; Marcelin Joanis; Andrea Lodi |
| Abstract: | This paper introduces the Minimum Price Markov Game (MPMG), a theoretical model that reasonably approximates real-world first-price markets following the minimum price rule, such as public auctions. The goal is to provide researchers and practitioners with a framework to study market fairness and regulation in both digitized and non-digitized public procurement processes, amid growing concerns about algorithmic collusion in online markets. Using multi-agent reinforcement learningdriven artificial agents, we demonstrate that (i) the MPMG is a reliable model for first-price market dynamics, (ii) the minimum price rule is generally resilient to non-engineered tacit coordination among rational actors, and (iii) when tacit coordination occurs, it relies heavily on self-reinforcing trends. These findings contribute to the ongoing debate about algorithmic pricing and its implications. Cet article présente le jeu du prix minimum de Markov (MPMG), un modèle théorique qui se rapproche raisonnablement des marchés réels qui suivent la règle du prix minimum, tels que les enchères publiques. L'objectif est de fournir aux chercheurs et aux praticiens un cadre pour étudier l'équité du marché et la réglementation dans les processus de marchés publics numériques et non numériques, dans un contexte de préoccupations croissantes concernant la collusion algorithmique sur les marchés en ligne. En utilisant des agents artificiels basés sur l'apprentissage par renforcement multi-agents, nous démontrons que (i) le MPMG est un modèle fiable pour la dynamique du marché au premier prix, (ii) la règle du prix minimum est généralement résistante à la coordination tacite non technique entre les acteurs rationnels, et (iii) lorsque la coordination tacite se produit, elle s'appuie fortement sur des tendances qui se renforcent d'elles-mêmes. Ces résultats contribuent au débat en cours sur la tarification algorithmique et ses implications. |
| Keywords: | Algorithmic Game Theory, Multiagent Reinforcement Learning, Algorithmic Coordination, Algorithmic Pricing, Théorie algorithmique des jeux, apprentissage par renforcement multi-agents, coordination algorithmique, tarification algorithmique |
| Date: | 2025–04–08 |
| URL: | https://d.repec.org/n?u=RePEc:cir:cirwor:2025s-07 |
| By: | Klinenberg, Danny; Berman, Eli; Klor, Esteban |
| Abstract: | Many applied economic studies aim to estimate strategic behavior through reaction curves. Examples include two-sided conflicts, or economic trade wars, and algorithmic pricing between firms. Analysis is usually performed at a prespecified time interval, such as days, weeks, months, or years, using a vector autoregression (VAR). Yet sides may respond within a day to one action, but wait a month after another. If data is recorded in arbitrary time intervals, then the researcher may mistake waiting to act for inaction. We analytically show that VAR analyses do not recover true reaction curves if the timing of reaction is not accurately recorded. This misspecification can cause the sign of the VAR coefficient to reverse and misspecified standard errors leading to erroneous inference. We discuss an alternative structural approach rooted in game theory to estimate reaction curves and investigate its usefulness in a Monte Carlo simulation. |
| Keywords: | Social and Behavioral Sciences, conflict, game theory, response time, econometrics, vector autoregression, reaction curve |
| Date: | 2025–04–01 |
| URL: | https://d.repec.org/n?u=RePEc:cdl:globco:qt50087695 |
| By: | Sinda Kassab; Huan Xie |
| Abstract: | We report a laboratory experiment on dynamic patent races in an indefinite horizon with complete information. In a competitive environment, we analyze the R&D investment behavior of players who are randomly and anonymously paired in each race. We vary subjects’ initial positions as leader/follower or symmetric/asymmetric, as well as the distance between the initial knowledge stock and the target. Our results show that individual average effort is highest for players in a tie position, followed by leaders, and lowest for followers. Starting as a follower (leader) leads to a lower (higher) chance of winning the race. Spillovers realized in the previous round significantly increase players’ investment in the current round. Convergence toward equilibrium play becomes more pronounced in the second half of the sessions. Efficiency loss is significantly higher in races starting from a symmetric position than from an asymmetric position and is also significantly higher in the low treatment than in the high treatment. Nous présentons une expérience de laboratoire sur les courses aux brevets dynamiques dans un horizon indéfini avec une information complète. Dans un environnement concurrentiel, nous analysons le comportement d'investissement en R&D des joueurs qui sont appariés de manière aléatoire et anonyme dans chaque course. Nous faisons varier les positions initiales des sujets (leader/suiveur ou symétrique/asymétrique), ainsi que la distance entre le niveau de connaissance initial et la cible. Nos résultats montrent que l'effort individuel moyen est le plus élevé pour les joueurs en position d'égalité, suivis par les leaders, et le plus faible pour les suiveurs. Commencer en tant que suiveur (leader) conduit à une chance plus faible (plus élevée) de gagner la course. Les retombées réalisées lors du tour précédent augmentent de manière significative l'investissement des joueurs dans le tour en cours. La convergence vers le jeu d'équilibre devient plus prononcée dans la seconde moitié des sessions. La perte d'efficacité est significativement plus élevée dans les courses commençant à partir d'une position symétrique qu'à partir d'une position asymétrique et est également plus élevée dans le traitement faible que dans le traitement élevé. |
| Keywords: | Patent race, absorptive capacity, knowledge accumulation, efficiency loss, experimental investigation, Course aux brevets, capacité d'absorption, accumulation de connaissances, perte d'efficacité, enquête expérimentale |
| Date: | 2025–04–08 |
| URL: | https://d.repec.org/n?u=RePEc:cir:cirwor:2025s-08 |