Infinitely-repeated Game Research Articles

Is high-intensity conflict escalation inevitable in the future? A two-level game analysis on the causes of US-Iran risky rivalry

In recent years, there appears to be a growing consensus among policymakers in both the East and the West, that the decades of global peace after the Cold War has now come to an end, and that the world is facing mounting security risks to the future of humanity. Among those challenges, the ongoing U.S.-Iran conflict poses particularly significant risks to regional and global security, and is closely related to many other contemporary international crises involving European states and their allies, particularly the Russo-Ukrainian War, the nuclear proliferation in Europe, and the military disputes between the Iran-backed Houthis and EU forces. But why has the U.S.-Iran relationship deteriorated so dramatically over the past years, and what are the future risks its presents to the international community? While extensive scholarly works have been conducted to examine the ideological, historical, and geopolitical variables that fuel this observed escalating antagonism, no study to date has formal-modelled the complex interactions between Tehran and Washington into a two-level game. Utilizing an infinitely-repeated game theory approach, this research presents a comprehensive analytical framework that explains how interrelated political factors at both the international and the domestic level jointly shape the dynamic of this bilateral relationship. We contend that the domestic rally effect created by risk-oriented diplomacy, incompatible ideological stances and political values, the increasing polarization within U.S. Congress, and the mounting rivalry between Israel and the Iran-led Axis of Resistance convince policymakers from both sides that their utilities can be maximized in a non-cooperative game. Based on our models, it can be forecasted that there is hardly any chance Washington and Tehran will concede to the other’s security demands in the foreseeable future. Thus, the risks of high-intensity conflict escalation due to miscalculation will continue to upsurge in the future.

CRRA utility and the sustainability of cooperation in infinitely-repeated games

In a symmetric infinitely-repeated game, where players have constant relative risk aversion (CRRA), or constant elasticity of intertemporal substitution, utility functions, it is shown that the critical discount factor required to sustain full cooperation is decreasing in the coefficient of relative risk aversion (increasing in the elasticity of intertemporal substitution). An application to cooperation in international environmental agreements (IEA) is presented and it is shown that the limit of the critical discount factor as the number of countries goes to infinity is equal to one (zero) if the coefficient of intertemporal inequality aversion is less (greater) than one. • Analyses infinitely-repeated game when players have CRRA utility functions. • Cooperation in infinitely-repeated games is easier the more risk-averse are players. • Application to International Environmental Agreement with many countries.

The emerging threat of artificial intelligence on competition in liberalized electricity markets: A deep Q-network approach

According to Sustainable Development Goals (SDGs), societies should have access to affordable, reliable, and sustainable energy. Liberalized electricity markets have been established to provide affordable electricity for end-users through advertising competition. Although these new markets are designed to serve competition, there are recorded incidents where participants abused their market power and disrupted the competition through collusion. Unfortunately, modern autonomous pricing algorithms may further assist myopic players to discover collusive strategies with a minimum amount of sensitive information. Therefore, in this study, we investigate the impact of emerging learning algorithms on the bidding strategies of Power Generating Companies (GenCos) and compare their performance against game-theoretic expectations. A novel deep Q-network (DQN) model is developed, by which GenCos determine the bidding strategies to maximize average long-term payoffs in a day-ahead market. The presented DQN model assumes that GenCos have no information regarding the rivals’ true generation costs and profits. To the best of the authors’ knowledge, this is the first study that thoroughly investigates players’ behavior utilizing a modern DQN model and compares its results with equilibria of the non-cooperative single-stage and infinitely-repeated games in the context of electricity markets. The outcomes articulate that GenCos equipped with advanced learning models may be able to collude unintentionally while trying to ameliorate long-term profits. Moreover, GenCos that employ the presented DQN model could discover and sustain more profitable (e.g., collusive) strategies vis-à-vis a conventional Q-learning method. Collusive strategies can lead to exorbitant electric bills for end-users, which is one of the influential factors in energy poverty. Thus, policymakers and market designers should be vigilant regarding the combined effect of information disclosure and autonomous pricing, as new models exploit information more effectively.

원청-하청 간 거래관행이 혁신에 미치는 영향: 독일ㆍ미국의 자동차산업을 중심으로 (On the Impact of the Supplier-Buyer Relation on Innovation: Lessons from the German and the U.S. Automobile Industry)

원청-하청 간 거래관행이 혁신에 미치는 영향: 독일ㆍ미국의 자동차산업을 중심으로 (On the Impact of the Supplier-Buyer Relation on Innovation: Lessons from the German and the U.S. Automobile Industry)

'Seemingly-Beneficial' Interventions

Organizations routinely introduce hitherto-unexplored interventions to improve their supply chains. Consider a principal (e.g., a firm) that implements a “seemingly-helpful” intervention: For any fixed actions of the principal and the agents (e.g., consumers), the principal’s payoff is higher in the presence of the intervention than in its absence. While one would expect such well-intentioned interventions to benefit the principal, several papers within the OM literature show that the principal's equilibrium payoff can be hurt, even ignoring the intervention’s implementation cost. While this conclusion is often based on analyzing a single-shot, simultaneous-move game, repeated-interactions can also serve as an appropriate environment in many cases. A fundamental question arises: Does this conclusion hold even under repeated interactions? We study this question using the framework of infinitely-repeated games and the notion of a precommitment equilibrium from the literature on reputation in repeated games. We identify two key characteristics that determine whether a seemingly-beneficial intervention helps, or can possibly hurt the firm: (a) nature of the intervention (ceteris paribus, does it induce agents to react in a manner favorable to the principal?), and (b) extent of interaction (single-shot at one extreme and infinitely-repeated at the other). Interestingly, we demonstrate the following two possibilities using settings analyzed in the recent OM literature: seemingly-beneficial interventions can (a) hurt the firm in a single-shot analysis but benefit under repeated interactions, and (b) continue to hurt the firm under repeated interactions. We also obtain easy-to-interpret conditions under which the benefit of such interventions is guaranteed under repeated interactions.

Design of a security-aware routing scheme in Mobile Ad-hoc Network using repeated game model

Security is a crucial factor in Mobile Ad hoc Networks (MANET) where inaccessible environments cause assorted categories of security intimidations to provide the malicious-free network. Game theory plays a crucial part in scheming well-organized security methodologies in computer networks. In this work, an Infinitely-repeated game and cooperation approach is designed to detect malicious nodes and also to enhance energy-efficiency. The goal of an Infinitely-repeated game aims to ensure the defector or malicious node in the network has a short run gain and a long-run loss. The prime objective of the proposed scheme is to attack detection and defense, accuracy for preventing the packet drops. The proposed method is verified via simulation.

Inefficient stage Nash is not stable

It is shown that, in infinitely-repeated games between two arbitrarily patient players, strategy profiles with inefficient pure stage-Nash continuations are not strategically stable (Kohlberg and Mertens, 1986). By contrast, a set of strategy profiles similar to the Prisoners' Dilemma's “perfect tit-for-tat” is “uniformly robust to perfect entrants” (Swinkels, 1992), and hence contains a strategically stable set. Moreover, this set satisfies iterated dominance and a version of forward induction, whilst its stable subset is admissible.

Sustainable agreements on stochastic river flow

Many river sharing agreements in transboundary river basins are inherently unstable. Due to stochastic river flow, agreements may be broken in case of drought. The objective of this paper is to analyze whether river sharing agreements can be self-enforcing, or sustainable. We do so using an infinitely-repeated sequential game that we apply to several classes of agreements. To derive our main results we apply the equilibrium concepts of subgame-perfect equilibrium and renegotiation-proof equilibrium to the river sharing problem. We show that, given the upstream–downstream asymmetry, sustainable agreements allow downstream agents to reap the larger share of the benefits of cooperation.

Endogenous Reputation Formation: Cooperation and Identity Under the Shadow of the Future

People are interacting more with strangers thanks to recent technological advancement in online platforms. Online interactions can be characterized by infinitely-repeated games. Recent studies have shown that institutions that make people’s decisions open to others may enhance cooperation in these situations. But it is still unknown whether people can successfully cooperate with each other by choosing to show their identities and building good reputation when there is an option to hide them. We deal with this question using an experimental laboratory. Our experiment shows that a non-negligible fraction of people conceal their identities and people fail to cooperate with each other if hiding identities is free. However, almost all show their identities and successfully achieve cooperation with their partners if a small explicit cost is charged for act of hiding.

Non Negative Benefits of the Commons in Infinitely Repeated Game

In this paper, two groups use the commons as a resource with its near-sightedness and far-sightedness. We study the game with majority of the group and unanimity of the group in its decision making. And we look into the game with the individuals’ utility in making use of the commons with near-sightedness and farsightedness in infinitely repeated game. SPE exists for nearsightedness which tends to destroy the commons in near large period of the game but farsightedness makes safe and useful for infinite period of the survivility of the humanity.

Debiasing Through Auction? Inertia in the Liberalization of Retail Markets

Abstract We analize a market in the process of liberalization. Consumers are biased in favor of the incumbent firm and we assume that they can discover the true value of new suppliers only by switching. In an infinitely-repeated game setting with Bertrand competition, we first show that efficient entry might not take place. We then evaluate the effect of organizing a public auction for assigning consumers to a “default supplier” and show that such a mechanism (which respects the freedom of choice by consumers) would support entry efficiency. However, auctioning might also increase inefficient, although temporary, entry. K EYWORDS : electricity retail, default supplier, entry, competition policy, universal service obligations. JEL Classification: D43, L13, L94 . % Authors are deeply indebted to Eileen Fumagalli, who was part of the original research project (the usual caveat applies). Financial supports by Regione Lombardia and Fondazione Alma Mater (Pavia) are gratefully acknowledged. * Statements and opinions expressed in this article are those of Clara Poletti and do not reflect the official position of the Autorita per l’energia elettrica e il gas.

The myth of the Folk Theorem

The Folk Theorem for repeated games suggests that finding Nash equilibria in repeated games should be easier than in one-shot games. In contrast, we show that the problem of finding any Nash equilibrium for a three-player infinitely-repeated game is as hard as it is in two-player one-shot games. More specifically, for any two-player game, we give a simple construction of a three-player game whose Nash equilibria (even under repetition) correspond to those of the one-shot two-player game. Combined with recent computational hardness results for one-shot two-player normal-form games ( Daskalakis et al., 2006; Chen et al., 2006; Chen et al., 2007), this gives our main result: the problem of finding an (epsilon) Nash equilibrium in a given n × n × n game (even when all payoffs are in { − 1 , 0 , 1 } ) is PPAD-hard (under randomized reductions).

A behavioral Laffer curve: Emergence of a social norm of fairness in a real effort experiment

This paper demonstrates, through a controlled experiment, that the “Laffer curve” phenomenon does not always reflect a conventional income - leisure trade-off. Whether out of reason or out of emotion, taxpayers may also be willing to punish intentionally unfair tax setters by working less than they would under the same exogenous circumstances. We conduct a real effort experiment in which a player A (the “tax receiver”) is matched with a player B (the “worker”) to elicit the conditions under which tax revenues will increase under a certain threshold and decrease thereafter. We ran four different treatments by manipulating work opportunities and the power to tax. Consistent with the history of tax revolts, the working partner overreacts to the perceived unfairness of taxation when the tax rate exceeds 50%, most strongly so in the high effort treatment. With two types of players, selfish and empathic, our model predicts the emergence of a social norm of fairness under asymmetric information, and elicits the optimal and emotional patterns of punishments and rewards consistent with the norm’s enforcement. The social norm allows players to coordinate tacitly on a “focal equilibrium”, which offers a solution to the indeterminacy raised by the Folk theorem for infinitely-repeated games and a behavioral justification for the tit-for-tat strategy. The social norm of fairness enhances productive efficiency in the long run.

A “Super” Folk Theorem for dynastic repeated games

We analyze dynastic repeated games. These are repeated games in which the stage game is played by successive generations of finitely-lived players with dynastic preferences. Each individual has preferences that replicate those of the infinitely-lived players of a standard discounted infinitely-repeated game. Individuals live one period and do not observe the history of play that takes place before their birth, but instead create social memory through private messages received from their immediate predecessors. Under mild conditions, when players are sufficiently patient, all feasible payoff vectors (including those below the minmax of the stage game) can be sustained by sequential equilibria of the dynastic repeated game with private communication. In particular, the result applies to any stage game with n ≥ 4 players for which the standard Folk Theorem yields a payoff set with a non-empty interior. We are also able to characterize fully the conditions under which a sequential equilibrium of the dynastic repeated game can yield a payoff vector not sustainable as a subgame perfect equilibrium of the standard repeated game. For this to be the case it must be that the players’ equilibrium beliefs violate a condition that we term “inter-generational agreement.”

Payment for Order Flow

We develop a dynamic model of price competition in broker and dealer markets. Competing market makers quote bid-ask spreads, and competing brokers choose commissions to be paid by an investor. Investors, who submit either market or limit orders, choose a broker to minimize total transaction costs. We model this as an infinitely-repeated game. With no payment for order flow, there exist equilibria in which brokers and market makers earn positive profits. There is also an equilibrium in which they earn zero profits. With payment for order flow, spreads widen to more than compensate for this payment. Hence, while positive profit equilibria continue to exist, there is no equilibrium in which market makers earn zero profits. While brokerage commissions for market orders can fall, the total transactions cost to submitting a market order remains positive. Hence, payment for order flow redistributes welfare from traders who demand liquidity to those who supply it. We determine the level of payment for order flow in equilibrium, and provide some comparative statics.

On economic incentive for quality upgrading

This paper shows that in duopolistic price competition, the high-cost firm can earn a higher profit by its ability to produce higher quality. Hence, cost advantage alone cannot guarantee the low-cost firm a higher profit in either the two-stage constituent game or the infinitely-repeated game. There exists at least one profit division which sustains collusion between the duopoly in both price and quality, where the high-cost firm enjoys a higher profit in a certain range of the cost difference. Also, firms enlarge their quality differentiation furthermore in the tacit collusion than in the noncooperative Nash equilibrium of the two-stage constituent game.

Infinitely-repeated games with endogenous discounting

The standard repeated game setting is changed by allowing one player to decide the time interval between repetitions. The resulting folk theorem states that any individually rational stage-game strategy combination can be repeated in equilibrium, with no threshold discount factor requirement.

Collusion in finitely-repeated oligopolies

Explaining collusion in infinitely-repeated oligopolies is problematic because of the backward induction argument. The usual response to this has been to consider infinitely-repeated games and treat these as approximations of long, finite repetitions or to introduce a modicum of irrationality in firm decision-making. The present paper explores a third avenue which introduces some extensive form structure to the Cournot game itself. Hence the supergame constructed in this paper is one in which the stage game is itself an extensive-form game. In particular, the stage game is a Cournot oligopoly in which firms can observe each others initial production and respond by producing more before the product is sold on the market. With this structure it is possible to devise a discriminating trigger strategy which generates collusive behaviour among fully rational firms with finite lives.

Renegotiation-proof equilibrium: Reply

We report a general theorem on sustaining cooperation in infinitely-repeated games when the possibility of renegotiation constrains punishments not to harm both players. This result generalizes observations recently reported by E. van Damme (Renegotiation-proof equilibria in repeated prisoner's dilemma, J. Econ. Theory 47 (1989), 206–217) for the Prisoner's Dilemma.

The Structure of Nash Equilibrium in Repeated Games with Finite Automata

The authors study the Nash equilibria of a two-person, infinitely-repeated game in which players' preferences depend on repeated game payoffs and the complexity of the strategies they use. The model considered is that of A. Rubinstein (1986). Necessary conditions on the structure of the equilibria are derived. These results place significant restrictions on equilibrium payoffs. The results suggest that the introduction of implementation costs results in a striking discontinuity in the Nash equilibrium sets in terms of strategies and payoffs. Copyright 1988 by The Econometric Society.