This paper shows that the college admissions model with responsive preferences is not always satisfactory for representing real college admissions markets. Simple examples are used to illustrate real situations, in which the knowledge of the preferences of the institutions over all possible assignments of candidates is necessary for the analysis of relevant problems for the markets under consideration

We use epistemic game theory to explore rationales behind cooperative behaviors in the finitely repeated Prisoner’s Dilemma. For a class of type structures that are sufficiently rich, the set of outcomes that can arise when each player i is rational and satisfies \((m_i-1)\)th order strong belief of rationality is the set of paths on which each player i defects in the last \(m_i\) rounds. We construct

The paper presents a model of two-speed evolution in which the payoffs in the population game (or, alternatively, the individual preferences) slowly adjust to changes in the aggregate behavior of the population. The model investigates how, for a population of myopic agents with homogeneous preferences, changes in the environment caused by current aggregate behavior may affect future payoffs and hence

In this paper, we analyse a variation of truel competitions in which each prospective player is represented by a node in a scale-free network. Without including any particular spatial arrangement of players, traditional game theory suggests that in many truel settings the strongest player often has the lowest probability of survival, a paradox that has been popularised by the term survival of the unfittest

In an equilibrium framework, we explore how players communicate in games with multiple Nash equilibria when messages that make sense are not ignored. Communication is about strategies and not about private information. It begins with the choice of a language, followed by a message that is allowed to be vague. We focus on equilibria where the sender is believed whenever possible, and develop a theory

In this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy á la Shitovitz (Econometrica 41:467–501, 1973), with agents’ measure space having both atoms and an atomless sector. We proceed by following the idea of Aubin (Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford, 1979) to allow for partial participation

The emperor sum of combinatorial games is discussed in this study. In this sum, a player moves arbitrarily many times in one component. For every other component, the player moves once at most. The \(\mathcal {P}\)-positions of emperor sums are characterized using a parameter referred to as \(\mathcal {P}\)-position length. An emperor sum is a \(\mathcal {P}\)-position if and only if every component

We consider the problem of fairly reallocating the individual endowments of a perfectly divisible good among agents with single-peaked preferences. As agents may have different individual endowments in this problem, the standard concept of envy-freeness cannot be applied directly. Thus, we propose a new concept of fairness, which we call envy-freeness for similarities. It requires that each agent whose

This paper explores the lattice-theoretic properties of the family of all partitions of an arbitrary state space. I discuss a duality correspondence connecting meets (finest common coarsening) and joins (coarsest common refinement) of families of partitions, which conforms to the natural order-theoretic representations of these two operations. The partition lattice turns out to fail to be a distributive

Two agents with a common prior on the possible states of the world participate in a process of information transmission, consisting of sharing posterior probabilities of an event of interest. Aumann’s Agreement Theorem implies that such a process must end with both agents having the same posterior probability. We show that the \(\ell _1\)-variation of the sequence of posteriors of each agent, obtained

This paper studies payoffs in subgame perfect equilibria of two-player discounted overlapping generations games with perfect monitoring. Assuming that mixed strategies are observable and a public randomization device is available, it is shown that sufficiently patient players can obtain any payoffs in the interior of the smallest rectangle containing the feasible and strictly individually rational

We provide a school choice model where the student priority orders for schools are allowed not to be total. We introduce a class of algorithms, each of which derives a student optimal stable matching once we have an initial stable matching, when the priorities are represented by partial orders. Since a method to derive a stable matching exists when the priorities are partial orders, we can use it to

We investigate the strategic behavior of firms in a Hotelling spatial setting. The innovation is to combine two important features that are ubiquitous in real markets: (1) the location space is two-dimensional, often with physical restrictions on where firms can locate; (2) consumers with some probability shop at firms other than the nearest. We characterise convergent Nash equilibria (CNE), in which

This paper explores the welfare implications of free entry when firms face known entry costs, but production costs are privately known. Upon entering, firms compete in prices to supply a homogeneous good. Our framework yields results that are more nuanced than those of the literature on social efficiency and entry, where there is either insufficient or excessive entry for all parameter values. With

The notion of communication equilibrium extends Aumann’s (J Math Econ 1:67–96, 1974, https://doi.org/10.1016/0304-4068(74)90037-8) correlated equilibrium concept for complete information games to the case of incomplete information. This paper shows that this solution concept has the following property: for the class of incomplete information games with compact metric type and action spaces, and with

Chakraborty and Harbaugh (Am Econ Rev 100(5):2361–2382, 2010) prove the existence of influential cheap talk equilibria in one sender one receiver games when the state is multidimensional and the preferences of the sender are state independent. We show that influential equilibria do not survive the introduction of any small degree of Harsanyi-uncertainty, i.e., uncertainty about the sender’s preferences

We prove that positive recursive general quitting games, which are quitting games in which (a) each player has a single quitting action and possibly several continue actions, (b) the stage payoff as long as quitting does not occur is 0, and (c) the payoff when quitting occurs is non-negative, admit a sunspot \(\varepsilon \)-equilibrium, for every \(\varepsilon > 0\).

We propose a new notion of farsighted pairwise stability for dynamic network formation which includes two notable features: consideration of intermediate payoffs and cautiousness. This differs from existing concepts which typically consider either only immediate or final payoffs, and which often require that players are optimistic in any environment without full communication and commitment. For arbitrary

We present a general existence result for a type of equilibrium in normal-form games, which extends the concept of Nash equilibrium. We consider nonzero-sum normal-form games with an arbitrary number of players and arbitrary action spaces. We impose merely one condition: the payoff function of each player is bounded. We allow players to use finitely additive probability measures as mixed strategies

In large quasilinear economies, we provide sufficient conditions to establish the nonemptiness of several versions of approximate interim cores with endogenous communication. This is done by proving nonemptiness of approximate ex post cores satisfying incentive compatibility. Our model features a finite number of agents whose information is exclusive, whom we shall term “monopolists of scarce information

Dubins and Savage (How to gamble if you must: inequalities for stochastic processes, McGraw-Hill, New York, 1965) found an optimal strategy for limsup gambling problems in which a player has at most two choices at every state x at most one of which could differ from the point mass \(\delta (x)\). Their result is extended here to a family of two-person, zero-sum stochastic games in which each player

A pebbling move refers to the act of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The goal of graph pebbling is: Given an initial distribution of pebbles, use pebbling moves to reach a specified goal vertex called the root. The pebbling number of a graph \(\pi (G)\) is the minimum number of pebbles needed so every distribution of \(\pi (G)\) pebbles can reach every

Using a simple game-theoretical model of contests, we compare the effort exerted by rugby teams under three different point systems used in tournaments around the world. We consider a point system that awards four points to the winning team, no points to the losing team, and two points to each team in a case of a draw. The other two point systems award bonus points depending on the final score. They

We analyze a subgame perfect equilibrium (SPE) of an extensive game with perfect information induced by the firm-oriented deferred acceptance (DA) algorithm in a one-to-one matching market between firms and workers. Our game repeats the following procedure until every firm in the market has a partner: (i) an unmatched firm strategically decides to which worker to make an offer or to exit the market

We consider a discrete-time dynamic search game in which a number of players compete to find an invisible object that is moving according to a time-varying Markov chain. We examine the subgame perfect equilibria of these games. The main result of the paper is that the set of subgame perfect equilibria is exactly the set of greedy strategy profiles, i.e. those strategy profiles in which the players

We consider the fair division of a set of indivisible goods where each agent can receive more than one good, and monetary transfers are allowed. We show that if there are at least three goods to allocate, no efficient solution is population monotonic (PM) on the superadditive Cartesian product preference domain, and the Shapley solution is not PM even on the submodular domain. Moreover, the incompatibility

An evasion differential game of one evader and many pursuers is studied. The dynamics of state variables \(x_1,\ldots , x_m\) are described by linear differential equations. The control functions of players are subjected to integral constraints. If \(x_i(t) \ne 0\) for all \(i \in \{1,\ldots ,m\}\) and \(t \ge 0\), then we say that evasion is possible. It is assumed that the total energy of pursuers

In this paper we propose a basic fixed-point theorem for correspondences inspired by Tarski’s intersection point theorem. This result furnishes an efficient tool to prove the existence of pure strategy Nash equilibria for two player games with possibly discontinuous payoffs functions defined on compact real intervals.

I characterize the individually-rational utilitarian bargaining solution by combining several classical axioms with a novel axiom, monotone step-by-step negotiations (monotone SSN). One of the axioms involved in the characterization is conflict freeness, which imposes Pareto optimality on problems that include their ideal point; when conflict freeness is replaced by weak Pareto optimality, only one

Let (N, v) be a cooperative game with transferable utility and \(F\subseteq 2^N\) an arbitrary set system, where F represents the set of feasible coalitions S whose worths v(S) are known. We introduce a game \((N,v_F)\) as follows. If \(S\in F\), then \(v_F(S)=v(S)\) and otherwise \(v_F(S)\) is defined such that S has zero Harsanyi dividend. By taking different F, this model produces some well-known

We consider sender–receiver games in which the sender has finitely many types and the receiver makes a decision in a compact set. The new feature is that, after the cheap talk phase, the receiver makes a proposal to the sender, which the latter can reject in favor of an outside option. We focus on situations in which the sender’s approval is absolutely crucial to the receiver, namely, on equilibria

We give very simple algorithms for best play in the simplest kind of Dots and Boxes endgames: those that consist entirely of loops and long chains. In every such endgame we compute the margin of victory, assuming both players maximize the numbers of boxes they capture, and specify a move that leads to that result. We improve on results by Buzzard and Ciere on the same problem: our algorithms examine

We consider the problem of allocating several homogeneous indivisible goods when monetary transfers among agents are possible. We study the possibility of constructing strategy-proof and Pareto efficient mechanisms on restricted domains of agents’ valuation profiles. We show that there is no strategy-proof and Pareto efficient mechanism under the weak domain condition that all agents’ sets of possible

We study zero-sum combinatorial games within the framework of so-called Richman auctions (Lazarus et al., in Games No Chance 29:439–449, 1996). We modify the alternating play scoring ruleset Cumulative Subtraction (Cohensius et al., in Electron J Combin 26(P4):52, 2019), to a discrete bidding scheme, similar to Develin and Payne (Electron J Combin 17(1):85, 2010). Players bid to move, and the player

The Goods and Services Tax (GST) Council of India has a non-conventional weighted voting procedure having a primary player who is a blocker and a set of secondary players. The voting weights are not fixed and are determined based on the subset of players which participate in the voting. We introduce the notion of voting schema to formally model such a voting procedure. Individual voting games arise

Monotonicity is an appealing principle of relational power measures in social networks. It states that as the influence of an individual changes, the relational power measure should change in the same direction. We axiomatically characterize the $$\beta $$ β - and score -measures on directed networks using three axioms: two different monotonicity axioms, the same symmetry axiom and two different efficiency

Recent advances in information and communication technologies have increased the incentives for firms to acquire information about rivals. These advances may have major implications for market entry because they make it easier for potential entrants to gather valuable information about, for example, an incumbent’s cost structure. However, little theoretical research has actually analyzed this question

We propose a simple model to investigate whether an agent works harder when she is informed of the tasks’ deadlines (i.e., under transparent management) or not (i.e., under opaque management). We do so in a stylized model where; (1) in each period, the agent may work at some cost, rather than shirk at no cost, so as to increase her probability of completing the task, (2) the agent receives an exogenous

This study examines how a CEO’s sensitivity affects information transmission from multiple unit managers when they communicate strategically during decision-making for technology investment. We develop a simple cheap talk model comprising one CEO and K unit managers, wherein the CEO makes a decision to maximize the units’ profit after the managers reveal their preference for the decision through cheap

We consider the problem of cleaning a transboundary river, proposed by Ni and Wang (Games Econ Behav 60:176–186, 2007). A river is modeled as a segment divided into subsegments, each occupied by one region, from upstream to downstream. The waste is transferred from one region to the next at some rate. Since this transfer rate may be unknown, the social planner could have uncertainty over each region’s

We study solutions that choose an interval of alternatives when agents have single-peaked preferences. Similar to Klaus and Storcken (2002), we ordinally extend these preferences over intervals. Loosely speaking, we extend the results of Moulin (1980) to our setting and show that the results of Ching (1997) cannot always be similarly extended. Our main results are the following. First, strategy-proofness

This paper extends the roommate problem to include externalities, allowing preferences for a partner to depend on the situation of others. Stability concepts for matchings and partitions of the set of agents are proposed and characterized, conditional on all agents having prudent expectations about other agents’ reactions to deviations. We prove that any roommate problem with externalities has a stable

We apply the classifier-Lasso (Su et al. 2016) to detect the presence of latent types in two data sets of previous contest experiments, one that keeps the grouping of contestants fixed over the experiment and one that randomly regroups contestants after each round. Our results suggest that there exist three distinct types of players in both contest regimes. The majority of contestants in fixed groups

We characterize three interrelated concepts in epistemic game theory: permissibility, proper rationalizability, and iterated admissibility. We define the lexicographic epistemic model for a game with incomplete information. Based on it, we give two groups of characterizations. The first group characterizes permissibility and proper rationalizability. The second group characterizes permissibility in

We study the existence of group strategy-proof stable rules in many to-many matching markets. We show that when firms have acyclical preferences over workers the set of stable matchings is a singleton, and the worker-optimal stable mechanism is a stable and group strategy-proof rule for firms and workers. Furthermore, acyclicity is the minimal condition guaranteeing the existence of stable and strategy-proof

In this paper we offer a new, unifying approach to modeling strategies of bounded complexity. In our model, the strategy of a player in a game does not directly map the set H of histories to the set of her actions. Instead, the player’s perception of H is represented by a map $$\varphi :H \rightarrow X,$$ where X reflects the “cognitive complexity” of the player, and the strategy chooses its mixed

The purpose of this paper is to study which coalition structures have stable distributions. We employ the projective core as a stability concept. Although the projective core is often defined only for the grand coalition, we define it for every coalition structure. We apply the core notion to a variety of economic models including the public goods game, the Cournot and Bertrand competition, and the

We justify risk neutral equilibrium bidding in commonly known fair division games with incomplete information in an evolutionary setup by postulating (i) minimal common knowledge assumptions, (ii) optimally responding agents to conjectural beliefs about how others behave and (iii) evolution of conjectural beliefs with fitness measured by expected payoffs. We axiomatically justify the game forms, derive

We investigate second-price sequential auctions of unit-demand bidders with time-variable valuations under complete information. We describe how a bidder figures willingness to pay by calculating option values, and show that when bidders bid their option value, and a condition of consistency is fulfilled, a subgame-perfect equilibrium is the result. With no constraints on valuations, equilibria are

I analyze the set of pure strategy subgame perfect Nash equilibria of any finitely repeated game with complete information and perfect monitoring. The main result is a complete characterization of the limit set, as the time horizon increases, of the set of pure strategy subgame perfect Nash equilibrium payoff vectors of the finitely repeated game. The same method can be used to fully characterize the

An issue game is a combination of a monotonic simple game and an issue profile. An issue profile is a profile of linear orders on the player set, one for each issue within the set of issues: such a linear order is interpreted as the order in which the players will support the issue under consideration. A power index assigns to each player in an issue game a nonnegative number, where these numbers sum

We give sufficient and necessary conditions for the non-emptiness of the alpha-core in the setting of strategic games with non-ordered and discontinuous preferences. In order to prove our results, we can avoid the use of Scarf’s Theorem for NTU-games, by suitably appealing to the Ky Fan minimax inequality. Examples clarify our conditions and allow the comparison of our results with the previous ones

This note shows that the work by Simon and Tomkowicz (Israel J Math 227(1):215–231, 2018) answers another outstanding open question in game theory in addition to the non-existence of approximate Harsanyi equilibrium in Bayesian games: it shows that strategic form games with bounded and separately continuous payoffs need not possess approximate equilibria.

We study first-price auctions in which the number of bidders is the seller’s private information, and investigate the use of a reserve price to signal this private information. We use the D1 criterion to refine the set of equilibria and characterize a symmetric separating equilibrium outcome, where the reserve price increases with the number of bidders. The key driving force is a certain form of single-crossing

We consider auctions where bidders have external incentives and focus on the case where their valuations in the auction are positively correlated with their productivity which matters in a second stage job market. We study how this affects bidding behavior and wages in the job market and proceed to test the model’s implication in an experiment where treatments differ according to which bids are disclosed

We follow the Nash program to provide a new strategic justification for the Talmud rule to solve bankruptcy problems. The design of our game is based on a focal characterization of the rule, obtained when combining consistency with two properties guaranteeing meaningful lower and upper bounds to all creditors.

We provide an exact analytical solution of the Nash equilibrium for the kth price auction by using inverse of distribution functions. As applications, we identify the unique symmetric equilibrium where the valuations have polynomial distribution, fat tail distribution and exponential distributions.

We study Tullock contests with n symmetric players. We show that in a contest without an exit option, if prizes and punishments (negative prizes) have the same cost, it is optimal for the designer who wants to maximize the players’ total effort to allocate the entire prize sum to a single punishment without any prize. On the other hand, in a contest with an exit option, it is optimal to allocate the

We prove some interesting properties of unilaterally competitive games when there are more than two players. We show that such games possess: (1) a Nash equilibrium, (2) maximin-solvability, (3) strong solvability in the sense of Nash, and (4) weak acyclicity, all in pure strategies of finite or infinite games.

We study strong Nash equilibria in mixed strategies in finite games. A Nash equilibrium is strong if no coalition of players can jointly deviate so that all players in the coalition get strictly better payoffs. Our main result concerns games with two players and states that if a game admits a strong Nash equilibrium, then the payoff pairs in the support of the equilibrium lie on a straight line in