P. Jean-Jacques Herings

Tilburg University | UVT

The notion of stationary equilibrium is one of the most crucial solution concepts in stochastic games. However, a stochastic game can have multiple stationary equilibria, some of which may be unstable or counterintuitive. As a refinement of stationary equilibrium, we extend the concept of perfect equilibrium in strategic games to stochastic games a...

We consider a group of receivers who share a common prior on a finite state space and who observe private correlated messages that are contingent on the true state of the world. Our focus lies on the beliefs of receivers induced via the signal chosen by the sender and we provide a comprehensive analysis of the inducible distributions of posterior b...

A sender wants to persuade multiple homogeneous receivers to vote in favor of a proposal. Before the vote sender commits to a signal which sends private, potentially correlated, messages to receivers that are contingent on the true state of the world. The best equilibrium for sender in the resulting incomplete information game is unappealing: all r...

We study bankruptcy problems in financial networks in the presence of general bankruptcy laws. The set of clearing payment matrices is shown to be a lattice, which guarantees the existence of a greatest clearing payment and a least clearing payment. Multiplicity of clearing payment matrices is both a theoretical and a practical concern. We present...

We consider financial networks where agents are linked to each other by financial contracts. A centralized clearing mechanism collects the initial endowments, the liabilities and the division rules of the agents and determines the payments to be made. A division rule specifies how the assets of the agents should be rationed. Since payments made dep...

We propose a solution concept for social environments called social rationalizability with mediation that identifies the consequences of common knowledge of rationality and farsightedness. In a social environment several coalitions may and could be willing to move at the same time. Individuals not only hold conjectures about the behaviors of other...

One of the most important stability concepts for network formation is pairwise stability. We develop a homotopy algorithm that is effective in computing pairwise stable networks for a generic network formation problem. To do so, we reformulate the concept of pairwise stability as a Nash equilibrium of a non-cooperative game played by the links in t...

The subgame perfect equilibrium in stationary strategies (SSPE) is the most important solution concept in applications of stochastic games, making it imperative to develop efficient methods to compute an SSPE. For this purpose, this paper develops an interior-point differentiable path-following method (IPM), which establishes a connection between a...

We propose a solution concept for social environments called social rationalizability with mediation that identifies the consequences of common knowledge of rationality and farsightedness. In a social environment several coalitions may and could be willing to move at the same time. Individuals not only hold conjectures about the behaviors of other...

We study subgame ϕ-maxmin strategies in two-player zero-sum stochastic games with a countable state space, finite action spaces, and a bounded and universally measurable payoff function. Here, ϕ denotes the tolerance function that assigns a nonnegative tolerated error level to every subgame. Subgame ϕ-maxmin strategies are strategies of the maximiz...

In a local interaction model agents play bilateral prisoners’ dilemmas with their immediate neighbors and have three possible strategies: altruistic, egoistic, and partial cooperation. After each period the agents adopt the strategy with the highest average payoff in their observed local neighborhood. There does not exist an absorbing state in whic...

We consider a matching with contracts model in which buyers face financial constraints. In this model, a competitive equilibrium may fail to exist. We therefore propose the new notion of quantity-constrained competitive equilibrium (QCCE). At a QCCE, buyers form expectations about the expected supply of trades. A buyer may expect that a trade is no...

We study the criminal networks that will emerge in the long run when criminals are neither myopic nor completely farsighted but have some limited degree of farsightedness. We adopt the horizon-K farsighted set to answer this question. We find that in criminal networks with n criminals, the set consisting of the complete network is a horizon-K farsi...

Farsighted economic agents can use their advantage to exploit their more myopic counterparts. In public goods games played on networks, such an agent will attempt to manipulate as many of his neighbors as possible to contribute to the public good. We study the exploitation of a myopic population by a single farsighted player in such games. We show...

We study bargaining models in discrete time with a finite number of players, stochastic selection of the proposing player, endogenously determined sets and orders of responders, and a finite set of feasible alternatives. The standard optimality conditions and system of recursive equations may not be sufficient for the existence of a subgame perfect...

We study the criminal networks that will emerge in the long run when criminals are neither myopic nor completely farsighted but have some limited degree of farsightedness. We adopt the horizon-K farsighted set of Herings, Mauleon and Vannetelbosch (2019) to answer this question. We …nd that in criminal networks with n criminals, the set consisting...

In cooperative games, the coalition structure core is, despite its potential emptiness, one of the most popular solutions. While it is a fundamentally static concept, the consideration of a sequential extension of the underlying dominance correspondence gave rise to a selection of non-empty generalizations. Among these, the payoff-equivalence minim...

At each moment in time, an alternative from a finite set is selected by a stochastic process. Players observe the selected alternative and sequentially cast a yes or a no vote. If the set of players casting a yes vote is decisive for the selected alternative, it is accepted and the game ends. Otherwise the next period begins. We refer to this class...

We consider marriage problems where myopic and farsighted players interact. To study such problems, we use the pairwise myopic-farsighted stable set. Blocking occurs by coalitions of size one or two. We require that all blocking players should strictly improve. We pay particular attention to the question whether core elements survive in this enviro...

We introduce the new notion of the pairwise myopic-farsighted stable set to study stable matchings under the assumption that players can be both myopic and farsighted. For the special case where all players are myopic, our concept predicts the set of matchings in the core. When all players are farsighted, we provide the characterization of pairwise...

We consider a group of receivers who share a common prior on a finite state space and who observe private correlated signals that are contingent on the true state of the world. We show that, while necessary, Bayes plausibility is not sufficient for a distribution over posterior belief vectors to be inducible, and we provide a characterization of in...

The most important rule to determine payments in real-life bankruptcy problems is the proportional rule. Many such bankruptcy problems are characterized by network aspects, and the values of the agents’ assets are endogenous as they depend on the extent to which claims on other agents can be collected. These network aspects make an axiomatic analys...

In the original publication of the article, the last name of the corresponding author was omitted by mistake. The correct name should read: P. Jean-Jacques Herings. The original article has been corrected.

This paper studies coalition formation among individuals who differ in productivity. We consider egalitarian societies in which coalitions split their surplus equally and individualistic societies in which coalitions split their surplus according to productivity. Preferences of coalition members depend on their material payoffs, but are also influe...

We study perfect information games played by an infinite sequence of players, each acting only once in the course of the game. We introduce a class of frequency-based minority games and show that these games have no subgame perfect ϵ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \u...

The paper considers a class of decision problems with an infinite time horizon that contains Markov decision problems as an important special case. Our interest concerns the case where the decision maker cannot commit himself to his future action choices. We model the decision maker as consisting of multiple selves, where each history of the decisi...

In cooperative games, the coalition structure core is, despite its potential emptiness, one of the most popular solutions. While it is a fundamentally static concept, the consideration of a sequential extension of the underlying dominance correspondence gave rise to a selection of non-empty generalizations. Among these, the payoff-equivalence mini...

We consider a Bertrand duopoly with homogeneous goods and we allow for asymmetric marginal costs. We derive the Myopic Stable Set in pure strategies as introduced by Demuynck et al. (Econometrica 87:111–138, 2019). In contrast to the set of Nash equilibria, the unique Myopic Stable Set can be easily characterized in closed form and it provides an i...

We introduce the concept of a horizon-K farsighted set to study the influence of the degree of farsightedness on network stability. The concept generalizes existing concepts where all players are either fully myopic or fully farsighted. A set of networks \(G_{K}\) is a horizon-K farsighted set if three conditions are satisfied. First, external devi...

This paper studies adaptive learning in the class of weighted network games. This class of games includes applications like research and development within interlinked firms, crime within social networks, the economics of pollution, and defense expenditures within allied nations. We show that for every weighted network game, the set of pure Nash eq...

We study games with almost perfect information and an infinite time horizon. In such games, at each stage, the players simultaneously choose actions from finite action sets, knowing the actions chosen at all previous stages. The payoff of each player is a function of all actions chosen during the game. We define and examine the new condition of ind...

We analyze the question of how to distribute the asset value of an insolvent firm among its creditors and the firm itself. Compared to standard bankruptcy games as studied in the game-theoretic literature, we treat the firm as a player and define a new class of transferable utility games called liability games. We show that the core of a liability...

This paper studies coalition formation among individuals who differ in productivity. The output of a coalition is determined by the sum of productivities if the coalition exceeds a minimal threshold of members. We consider competitive societies in which the surplus of a coalition is split according to productivity and egalitarian societies in which...

We introduce a new solution concept for models of coalition formation, called the myopic stable set (MSS). The MSS is defined for a general class of social environments and allows for an infinite state space. An MSS exists and, under minor continuity assumptions, it is also unique. The MSS generalizes and unifies various results from more specific...

The paper considers a matching with contracts model in the presence of price controls. The model contains two important streams in the matching literature, those with and those without monetary transfers, as special cases. An adjustment process that ends with a stable outcome is presented. The paper presents a notion of competitive equilibrium, cal...

We study the division of a surplus under majoritarian bargaining in the three-person case. In a stationary equilibrium as derived by Baron and Ferejohn (1989), the proposer offers one third times the discount factor of the surplus to a second player and allocates no payoff to the third player, a proposal which is accepted without delay. Laboratory...

We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents’ assets might be insufficient to satisfy their liabilities, leading to defaults. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. A clearing payment matrix is a payment matrix consistent...

This paper uses a dynamic stochastic model to solve for the optimal pricing policy of music recordings in the presence of P2P file-sharing networks eroding their sales. We employ a policy iteration algorithm on a discretized state space to numerically compute the optimal pricing policy. The realistically calibrated model reflects the real-world fig...

In an infinite horizon inventory and sales model, we show that the seller’s unique strategy exhibits increasing prices under general conditions on the revenue function. An increasing discount rate leads to an increase of the time interval between order times, but an increase in batch size has an ambiguous effect.

We study stable sets for marriage problems under the assumption that players can be both myopic and farsighted. We introduce the new notion of the myopic-farsighted stable set, which is based on the notion of a myopic-farsighted improving path. A myopic-farsighted stable set is the set of match-ings such that there is no myopic-farsighted improving...

We consider n-player perfect information games with payoff functions having a finite image. We do not make any further assumptions, so in particular we refrain from making assumptions on the cardinality or the topology of the set of actions and assumptions like continuity or measurability of payoff functions. We show that there exists a best respon...

We study von Neumann Morgenstern stable sets for one-to-one matching problems under the assumption of coalitional sovereignty (C), meaning that a deviating coalition of players does not have the power to arrange the matches of agents outside the coalition. We study both the case of pairwise and coalitional deviations. We argue further that dominanc...

We study stable sets for marriage problems under the assumption that players can be both myopic and farsighted. We introduce the new notion of the pairwise myopic-farsighted stable set. For the special cases where all players are myopic and where all players are farsighted, our concept predicts the set of matchings in the core. When all men are myo...

We consider a situation in which agents have mutual claims on each other, summarized in a liability matrix. Agents' assets might be insufficient to satisfy their liabilities leading to defaults. In case of default, bankruptcy rules are used to specify the way agents are going to be rationed. A clearing payment matrix is a payment matrix consistent...

We analyze the Condorcet paradox within a strategic bargaining model with majority voting, exogenous recognition probabilities, and no discounting for the case with three players and three alternatives. Stationary subgame perfect equilibria (SSPE) exist whenever the geometric mean of the players’ risk coefficients, ratios of utility differences bet...

We study centipede games played by an infinite sequence of players. Following the literature on time–inconsistent preferences, we distinguish two types of decision makers, naive and sophisticated, and the corresponding solution concepts, naive ϵ-equilibrium and sophisticated ϵ-equilibrium. We show the existence of both naive and sophisticated ϵ-equ...

We study von NeumannMorgenstern stable sets for one-to-one matching problems under the assumption of coalitional sovereignty, meaning that a deviating coalition of players does not have the power to arrange the matches of agents outside the coalition. We study both the case of pairwise and coalitional deviations. We argue further that dominance has...

We study von NeumannMorgenstern stable sets for one-to-one matching problems under the assumption of coalitional sovereignty, meaning that a deviating coalition of players does not have the power to arrange the matches of agents outside the coalition. We study both the case of pairwise and coalitional deviations. We argue further that dominance has...

The paper considers a class of decision problems with in_nite time horizon that contains Markov decision problems as an important special case. Our interest concerns the case where the decision maker cannot commit himself to his future action choices. We model the decision maker as consisting of multiple selves, where each history of the decision p...

The most important rule to determine payments in real-life bankruptcy problems is the proportional rule. Many bankruptcy problems are characterized by network aspects and default may occur as a result of contagion. Indeed, in financial networks with defaulting agents, the values of the agents' assets are endogenous as they depend on the extent to w...

We study strategies with one-period recall in the context of a general class of multilateral bargaining games. A strategy has one-period recall if actions in a particular period are only conditioned on information in the previous and the current period. We show that if players are sufficiently patient, given any proposal in the space of possible ag...

Network formation among individuals constitutes an important part of many OR processes, but relatively little is known about how individuals make their linking decisions in networks. This article provides an investigation of heuristic effects in individual linking decisions for network formation in an incentivized lab-experimental setting. Our mixe...

We study the implications of procedural fairness on the share of income that should be redistributed. We formulate procedural fairness as a particular non-cooperative bargaining game and examine the stationary subgame perfect equilibria of the game. The equilibrium outcome is called tax equilibrium and is shown to be unique. The procedurally fair t...

We study unanimity bargaining on the division of a surplus in the presence of monotonicity constraints. The monotonicity constraints specify a complete order on the players, which has to be respected by the shares in the surplus the players obtain in any bargaining outcome. A player higher in the order should not receive a lower share of the surplu...

In the literature, various models of games with restricted cooperation can be found. In those models, instead of allowing for all subsets of the set of players to form, it is assumed that the set of feasible coalitions is a subset of the power set of the set of players. In this paper, we consider such sets of feasible coalitions that follow from a...

The paper considers a one-to-one matching with contracts model in the presence of price controls. This set-up contains two important streams in the matching literature, those with and those without monetary transfers, as special cases and allows for intermediate cases with some restrictions on the monetary transfers that are feasible. An adjustment...

We study centipede games played by an infinite sequence of players. Following the literature on time-inconsistent preferences, we distinguish two types of decision makers, naive and sophisticated, and the corresponding solution concepts, nave -equilibrium and sophisticated -equilibrium. We show the existence of both naive and sophisticated -equilib...

We study strategic negotiation models featuring costless delay, general recognition procedures, endogenous voting orders, and finite sets of alternatives. Two examples show 1. non-existence of stationary subgame-perfect equilibrium SSPE. 2. the recursive equations and optimality conditions are necessary for SSPE but insufficient because these equat...

We consider n–player perfect information games with payoff functions having a finite image. We do not make any further assumptions, so in particular we refrain from making assumptions on the cardinality or the topology of the set of actions and assumptions like continuity or measurability of payoff functions. We show that there exists a best respon...

Risk allocation games are cooperative games that are used to attribute the risk of a financial entity to its divisions. In this paper, we extend the literature on risk allocation games by incorporating liquidity considerations. A liquidity policy specifies state-dependent liquidity requirements that a portfolio should obey. To comply with the liqui...

We consider a non-cooperative multilateral bargaining game and study an action-dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector-becomes-proposer protocol. We...