The role of strategic uncertainty in games: An experimental study of cheap talk and contracts in the Nash demand game

We utilise results from a human-subjects experiment to examine the connection between strategic uncertainty and outcomes in games. Our basic game is a Nash demand game where one player has an outside option available. A “chat” treatment allows bargainers to send cheap-talk messages prior to playing the basic game, and in a “contracts” treatment, they can additionally propose and accept binding contracts. We propose that strategic uncertainty comprises at least two facets: “coordination-type”, which is lower in the chat game than in the basic game, and “rationality-type”, which is lower in the contracts game than in the chat game. We find that both types of strategic uncertainty impact bargaining outcomes: moving from the basic game to the chat game, and thence to contracts, improves several aspects of outcomes, such as higher efficiency, less opting out and less under-demanding. Other results include a treatment effect on the types of agreements that are reached.     

Universality of Nash components

We show that Nash equilibrium components are universal for the collection of connected polyhedral sets. More precisely for every polyhedral set we construct a so-called binary game—a game where all players have two pure strategies and a common utility function with values either zero or one—whose success set (the set of strategy profiles where the maximal payoff of one is indeed achieved) is homeomorphic to the given polyhedral set. Since compact semi-algebraic sets can be triangulated, a similar result follows for the collection of connected compact semi-algebraic sets.We discuss implications of our results for the strategic stability of success sets, and use the results to construct a Nash component with index k for any fixed integer k.     

Non-Laplacian beliefs in a global game with noisy signaling

In standard global games, individual behavior is optimal if it constitutes a best response to agnostic—Laplacian—beliefs about the aggregate behavior of other agents. This paper considers a standard binary action global game augmented with noisy signaling by an informed policy-maker and shows that in this game, equilibrium beliefs depart in quite stark ways from the Laplacian benchmark. In the limit as signals become arbitrarily precise, so that all fundamental uncertainty is removed (leaving only strategic uncertainty), the equilibrium beliefs of the marginal individual concerning the aggregate action collapse to a discrete Bernoulli distribution, giving probability mass only to the polar extreme outcomes. By contrast in the underlying standard global game the marginal individual believes the aggregate action has a continuous uniform distribution, giving equal likelihood to all possible outcomes.     

Heterogeneity,impatience, and dynamic private provision of a discrete public good

We analyze dynamic private provision of a discrete public good by heterogeneous agents, who differ in terms of their levels of impatience, in a differential game framework. In contrast to the strategic complementarity result for homogeneous individuals, we show that an asymmetric completion Markov perfect equilibrium exists, where the individual contributions and the strategic behaviors depend crucially on an impatience differential: the difference in rates of time preference across groups of individuals. When this differential is insignificant, contributions of both types of individuals are strategic complements. On the other hand, when this impatience differential exceeds a threshold, the contributions of impatient individuals become strategic substitutes, whereas the contributions of patient individuals remain strategic complements. We show that group size has an interesting role to play in the strategic behavior: increasing the number of patient individuals aggravates the incentives to free‐ride by the impatient agents. We also derive a condition under which all the socially beneficial projects get completed in the equilibrium.     

Strategic complementarities and search market equilibrium

In this paper, we apply supermodular game theory to the equilibrium search literature with sequential search. We identify necessary and sufficient conditions for the pricing game to exhibit strategic complementarities and prove existence of equilibrium. We then show that price dispersion is inherently incompatible with strategic complementarities in the sense that the Diamond Paradox obtains when firms are identical and is robust within the class of search cost densities that are small near zero and support strategic complementarities. We also show that a major criticism of the literature, that agents act as if they know the distribution of prices, can be justified in the sense of convergent best response dynamics.     

Do people make strategic commitments? Experimental evidence on strategic information avoidance

Game theory predicts that players make strategic commitments that may appear counter-intuitive. We conducted an experiment to see if people make a counter-intuitive but strategically optimal decision to avoid information. The experiment is based on a sequential Nash demand game in which a responding player can commit ahead of the game not to see what a proposing player demanded. Our data show that subjects do, but only after substantial time, learn to make the optimal strategic commitment. We find only weak evidence of physical timing effects.     

A note on network formation with decay

This paper studies an endogenous network formation with decay. We introduce a strategic form game based on a simple bilateral cost allocation rule. We show that a strong Nash equilibrium of this game always exists and necessarily achieves efficient networks.     

Team reasoning without a hive mind

The theory of team reasoning has been developed to resolve a long-lasting niggle in orthodox game theory. Despite its intuitive appeal, the theory has received little attention from mainstream game theorists and economists to date. We believe that this is so because of two theoretic issues, which the theory of team reasoning itself needs to resolve. One of these presents a worry that the theory achieves its explanatory and predictive success by abandoning ontological individualism — a fundamental precept in mainstream economics, including game theory. Here we argue that the theory of team reasoning is compatible with ontological individualism. We show that the core principles of the theory — those that give rise to the above worry — are in fact implicitly assumed in some branches of orthodox game theory itself. We also argue against the methodological approach that construes team reasoning as involving a transformation of the interacting players’ payoffs in modelled games.     

Strategic approximations of discontinuous games

An infinite game is approximated by restricting the players to finite subsets of their pure strategy spaces. A strategic approximationof an infinite game is a countable subset of pure strategies with the property that limits of all equilibria of all sequences of approximating games whose finite strategy sets eventually include each member of the countable set must be equilibria of the infinite game. We provide conditions under which infinite games admit strategic approximations.     

Behavioral spillovers and cognitive load in multiple games: An experimental study

We present evidence from laboratory experiments of behavioral spillovers and cognitive load that spread across strategic contexts. In the experiments, subjects play two distinct games simultaneously with different opponents. We find that the strategies chosen and the efficiency of outcomes in one game depends on the other game that the subject plays, and that play is altered in predictable directions. We develop a measure of behavioral variation in a normal form game, outcome entropy, and find that prevalent strategies in games with low outcome entropy are more likely to be used in the games with high outcome entropy, but not vice versa. Taken together, these findings suggest that people do not treat strategic situations in isolation, but may instead develop heuristics that they apply across games.     

The tragedy of the commons revisited: The importance of group decision-making

We use a laboratory experiment to compare the way groups and individuals behave in an inter-temporal common pool dilemma. The experimental design distinguishes between a non-strategic problem where players (individuals or groups of three) make decisions without interaction and a strategic part where players harvest from a common pool. This allows us to correct for differences between individuals and groups in the quality of decisions when testing for differences in competitiveness. Group decisions are either made by majority rule or unanimity. The results show that groups are less myopic than individuals (i.e., they make qualitatively better decisions) but that they are more competitive than individuals when placed in a strategic setting. The net result for groups deciding by majority rule is that they make less efficient decisions in the strategic game than individuals do. We are able to show that this is caused by the median voter departing from her original preference in early periods with a shrinking pool. When groups have to make unanimous decisions they start playing the strategic game more efficiently then individuals do, but they rapidly become more competitive with repetition of the game.     

Extensive and strategic forms: Games and models for games

This paper aims to make precise, in the context of epistemic models for games, some relations between the normal or strategic form representation of a game and the extensive or dynamic form representation. It is argued, first, that epistemic models defined for strategic form representations provide all the materials necessary for defining models for corresponding extensive form representations of the game, models that provide information about the way the game is played that is sufficient to evaluate the rationality of the choices that the players make, and are disposed to make, in the course of playing the dynamic game. Second, two definitions of rationality are compared — one for strategy choices in the normal form representation, and one for the individual choices that the player is disposed to make in the course of playing the dynamic game. It is shown that they are essentially equivalent in games with perfect recall. The main focus is on the intuitive foundational assumptions about rationality and dynamic choice that are needed to motivate the definitions. It is argued that to evaluate the rationality of a player's choices in a dynamic context, it is essential to distinguish passive knowledge (knowledge about nature and about the prior beliefs and strategy choices of other players that is based on observation and inference) fromactive knowledge (knowledge about one's own choices and future choices that is grounded in one's decisions).     

OWNERSHIP VERSUS TIMING OF THE GAME

This study examines the impact of timing of the game on the welfare gains of privatisation in the presence of strategic trade policy. We argue that only if the public enterprise acts as a Cournot player will it generate an additional distortion that could outweigh the distortion caused by the oligopolistic behaviour of private firms. But with a first-mover advantage it can serve as an effective regulatory device comparable with a production subsidy. We further show that, in the presence of strategic trade policy, Cournot assumptions are inconsistent with the firms' preferences over the timing of the game. As public Stackelberg leadership is a subgame Nash equilibrium of the extended game with endogenous order of moves, we conclude that it is the timing of the game rather than firms' ownership structure which is responsible for the inefficiency of an international mixed market found by earlier studies.     

Competition Policy as Strategic Trade with Differentiated Products

The paper analyzes how countries use competition policy as a tool for strategic trade. In the model, two countries export to a third country. Each exporting country is endowed with a set of differentiated products. Each government chooses the number of exporters for its country and the products that each exporter sells in the first period, and a tax policy in the second period. Firms choose prices or quantities independently in the third period. In the unique subgame‐perfect equilibrium, both countries group all their products within a single firm—the “national champion policy.” We study the implication of different assumptions about the timing of the game.     

Markets for contracts: experiments exploring the compatibility of games and markets for games

Summmary. The research explores the relationship between games and the economic environment in which the games might be embedded. The focus is on a market institution in which agents buy and sell rights to participate in a follow-on stage of strategic interaction. The central question posed concerns how two different types of processes, the game and the market, interact. The market converges to a competitive equilibrium that is consistent with the Nash equilibrium that obtains in the game, and the convergence of the market to a competitive equilibrium lags the convergence of behaviors in the game to a Nash equilibrium.     

The inflation tax in an open economy with imperfect competition

This paper studies the national welfare maximizing inflation tax in an open economy with imperfect competition. It shows that the presence of a monopolistic distortion dampens the incentive to engage in strategic use of the inflation tax. If this dampening effect is strong enough, monetary policy becomes completely inward-looking, restoring the Friedman rule as an equilibrium strategy regardless of the actions of the foreign government. This aspect of the policy interaction—driven entirely by the presence of imperfect competition—is important because it determines the underlying structure of the policy game and is therefore crucial for determining whether or not there exist welfare gains from international monetary cooperation.     

Indirect reciprocity and strategic reputation building in an experimental helping game

We study indirect reciprocity and strategic reputation building in an experimental helping game. At any time only half of the subjects can build a reputation. This allows us to study both pure indirect reciprocity that is not contaminated by strategic reputation building and the impact of incentives for strategic reputation building on the helping rate. We find that pure indirect reciprocity exists, but also that the helping decisions are substantially affected by strategic considerations. Finally, we find that strategic do better than non-strategic players and non-reciprocal do better than reciprocal players, casting doubt on previously proposed evolutionary explanations for indirect reciprocity.     

Indirect reciprocity and strategic reputation building in an experimental helping game

We study indirect reciprocity and strategic reputation building in an experimental helping game. At any time only half of the subjects can build a reputation. This allows us to study both pure indirect reciprocity that is not contaminated by strategic reputation building and the impact of incentives for strategic reputation building on the helping rate. We find that pure indirect reciprocity exists, but also that the helping decisions are substantially affected by strategic considerations. Finally, we find that strategic do better than non-strategic players and non-reciprocal do better than reciprocal players, casting doubt on previously proposed evolutionary explanations for indirect reciprocity.     

Do cheaters in the lab also cheat in the field?

In this paper, we study the correlation between cheating in the lab and cheating in the field. We conduct a laboratory experiment using a variant of the Mind game (Jiang, 2013). Payoffs above a certain threshold are indicative of cheating behavior. Subjects are paid their earnings by bank transfer. A fraction of the subjects is deliberately paid more than their earnings. We send subjects a reminder e-mail stating their earnings and asking them if they have received their payment. We find a significant correlation of 0.31 between cheating in the lab and in the field. Subjects with higher payoffs in the Mind game are also less likely to report the overpayment. Our results speak to the lab-field generalizability of cheating behavior.     

ENDOGENOUS TIMING IN MULTI-STAGE DUOPOLY GAMES*

This paper presents an investigation of the endogenous timing in multi-stage duopoly games in which duopolists choose two variables over two periods. The paper elaborates the two-stage strategic commitment game discussed by Brander and Spencer (1983). Duopolists decide their outputs and cost-reducing investments and they are allowed to choose which action to take first. The paper discusses two types of games; one is a three-stage game in which each duopolist can commit to the order of choices before it chooses its output or cost-reducing investments, and the other is a two-stage game in which it cannot. The paper finds that at least one firm chooses its output first. Furthermore, the three-stage game has the unique equilibrium outcome in which both firms choose their outputs first.