The Effect of Subtracting a Constant from all Payoffs in a Hawk‐Dove Game: Experimental Evidence of Loss Aversion in Strategic Behavior

Economists and psychologists have documented patterns of individual decision‐making behavior (e.g., loss aversion) whereby losses and gains are treated differently. However, there has been little evidence of such patterns in multiplayer games. I report results showing the strongest evidence I know of that this phenomenon is present in games. Experimental subjects play two hawk‐dove games that are identical up to a constant; in one, all payoffs are positive, while in the other, payoffs are negative if and only if both players choose “hawk.” Under both fixed pairs and random matching, differences between the games are substantial, significant, and consistent with loss aversion.     

On payoff heterogeneity in games with strategic complementarities

Recent papers involving binary choices have argued that increasingheterogeneity decreases positive feedback. We show that no suchresult holds in models where all agents make interior choices.The results in the binary choice case arise for two reasons.First, if we increase heterogeneity without limit but imposea bounded choice set, then almost all players eventually becomecompletely unresponsive, preferring some corner so stronglythat they do not react to any feasible change in the behaviorof others. Second, discrete choice permits the constructionof strong, but fragile, positive feedbacks through compositioneffects.     

Monotone strong increases in risk and their comparative statics

We introduce a new concept of the monotone strong increase in risk (MSIR) order that imposes monotonicity restrictions on the ratio of the two cumulative of cumulative distribution functions as a special case of Rothschild–Stiglitz increases in risk that is the subset of the second‐degree stochastic dominance criterion. We show that the MSIR order implies that the conditional expectation of a random variable under one cumulative distribution function is greater than or equal to that under another cumulative distribution function. Restricting the payoff function to be linear in the random variable and limiting our analysis to risk‐averse decision‐makers who are prudent, we obtain appealing comparative statics results for the MSIR shift. This general conclusion can be applied to prevailing economic models having a linear payoff.     

Provision versus Appropriation in Symmetric and Asymmetric Social Dilemmas

Social dilemmas characterize decision environments in which individuals' exclusive pursuit of their own material self‐interest can produce inefficient allocations. Social dilemmas are most commonly studied in provision games, such as public goods games and trust games, in which the social dilemma can be manifested in foregone opportunities to create surplus. Appropriation games are sometimes used to study social dilemmas that can be manifested in destruction of surplus, as is typical in common‐pool resource extraction games. A central question is whether social dilemmas are more serious for inhibiting creation of surplus or in promoting its destruction. This question is addressed in this study with an experiment involving three pairs of payoff‐equivalent provision and appropriation games. Some game pairs are symmetric, whereas others involve asymmetric power relationships. We find that play of symmetric provision and appropriation games produces comparable efficiency. In contrast, power asymmetry leads to significantly lower efficiency in an appropriation game than in a payoff‐equivalent provision game. This outcome can be rationalized by reciprocal preference theory but not by models of unconditional social preferences.     

The Impact of Early Commitment on Games Played: Evidence from College Football Recruiting

We use data on athletic scholarship acceptance decisions to show that high school football players signal their ability level by delaying commitment. Although colleges can obtain information about student athletes, National Collegiate Athletic Association regulations limit information flow, making private information an important component of the scholarship market. Using ordinary least squares, censored regression, and negative binomial estimation, we show that for a given observed ability level, committing to a scholarship offer early is associated with less playing time after acceptance. In one season and at a typical average early signing date, early‐committing athletes played in 0.21 fewer games per season, or about 4% of the average number of games played.     

Incorporating fairness in generalized games of matching pennies

We examine individual behavior in generalized games of matching pennies. We have three main findings. First, individuals cooperate in these games; that is, they systematically select strategies that lead both players to obtain higher expected payoffs than in a Nash equilibrium. Second, existing models that assume altruistic preferences do not explain the cooperative behavior in these games. Third, among the main models in the extant literature, the only one that predicts the observed behavior is the quantal response equilibrium.     

Is the “smoke-filled room” necessary? An experimental study of the effect of communication networks on collusion

We investigate how well firms can collude with partial communication in relation to full communication. We find that firms vary their communication strategies with network structures. In the networks that have either an isolated firm or full communication, more players send “pure promises” suggesting everyone select the collusive actions unconditionally. In the network with leadership, more players send a “promise and threat” which includes a reward for collusion and a punishment for deviating. Because of the inability to communicate in the network with the isolated firm and the high frequency of deviation and punishment in the network with leadership, the full communication network achieves significantly higher payoff than partial communication.     

Mixed strategy equilibria in repeated games with one-period memory

Infinitely repeated games is the pre-dominant paradigm within which economists study long-term strategic interaction. The standard framework allows players to condition their strategies on all past actions; that is, assumes that they have unbounded memory. That is clearly a convenient simplification that is at odds with reality. In this paper we restrict attention to one-period memory and characterize all totally mixed equilibria. In particular, we focus on strongly mixed equilibria. We provide conditions that are necessary and sufficient for a game to have such an equilibrium. We further demonstrate the exact set of payoffs that can be generated by such equilibria.     

Noncooperative foundations for the kalai-smorodinsky and equal sacrifice solutions via prominence structures

In bargaining, players may adopt different prominence structures when making demands: (i) each player might use (1/N)th of his maximum monetary payoff as the prominence level or (ii) players might use a common prominence level. This paper considers a scheme in which players alternate making demands. It turns out that if the prominence levels described by (i) are used and if players have utilities linear in money, the outcome of this scheme converges to that of the Kalai-Smorodinsky solution as players' prominence levels get smaller. If the common prominence level of (ii) is used and if players have identical constant marginal utilities of money, the outcome of this scheme converges to that of the equal sacrifice solution as that prominence level gets smaller.     

The Costs of Increasing Transparency

In their seminal paper, Morris and Shin (Amer Econ Rev 92(5): 1521–1534, 2002a) argued that increasing the precision of public information is not always beneficial to social welfare. Svensson (Amer Econ Rev 96: 448–451, 2006) however has disputed this by saying that although feasible, the conditions for which this was true, were not all that likely. In that respect, therefore, increasing ‘transparency’ remains most of the times beneficial to social welfare. In this paper, we extend the Morris and Shin attempt by setting it up as an explicit interactive game between the Central Bank, the objectives of which we model explicitly, and the private sector. We show that in the absence of costs, both players benefit from transparency in the manner described previously in the literature, and point the differences in their gains. Following that, we then introduce the fact that increasing transparency comes at some costs and show how both players face incentives to free ride on each other as a result. The presence of costs thus alters the way in which greater transparency is attained.

Some rationalizability results for dynamic games

We study the relation between dynamical systems describing the equilibrium behavior in dynamic games and those resulting from (single‐player) dynamic optimization problems. More specifically, we derive conditions under which the dynamics generated by a model in one of these two classes can be rationalized by a model from the other class. We study this question under different assumptions about which fundamentals (e.g. technology, utility functions and time‐preference) should be preserved by the rationalization. One interesting result is that rationalizing the equilibrium dynamics of a symmetric dynamic game by a dynamic optimization problem that preserves the technology and the utility function requires a higher degree of impatience compared to that of the players in the game.     

Relative Responsiveness of Bargaining Solutions to Changes in Status-quo Payoffs

It is a well-known fact that several prominent bargaining solutions are responsive to changes in status-quo (i.e., disagreement or fallback) payoffs. When an agent’s status-quo payoff increases, his solution payoff either stays the same or increases. A fully general result for these solutions’ status-quo point ranking is impossible to establish. In this paper, using an important class of bargaining problems, a ranking of the relative status-quo point responsiveness of prominent bargaining solutions is obtained. Using the Constant Elasticity of Substitution class of bargaining problems, regardless of the concavity of the Pareto frontier and the level of increase in one’s status-quo payoff, we find the equal gains solution is the most responsive with respect to changes in status-quo payoffs, followed by the Nash solution. The equal sacrifice solutions is the least responsive, followed by the Kalai/Smorodinsky solution.

Fiscal Policy and Macroeconomic Stabilizations: What are the Gains from Cooperation?

In this paper we extend the open-economy stochastic framework of Obstfeld and Rogoff (Q J Econ. 117:503–36, 2002) to include distortionary taxation, when prices are flexible but wages are sticky. We use the model to analyze the optimal design of tax rules that respond to productivity shocks, under non-cooperation and cooperation between the fiscal authorities, and evaluate the gains from coordination. We show that, although monetary policy would be preferred to fiscal policy as a stabilization tool both under competition (Nash) and under cooperation, there is a role for procyclical fiscal stabilization in a monetary union where the monetary authority cannot respond to asymmetric shocks. Moreover, we show that in the Nash game there will be an incentive for the fiscal authorities to try to manipulate the terms-of-trade in their favor, and we estimate the potential gains from fiscal policy coordination. The size of the gains depends crucially on the value of the Frisch elasticity of labor supply. For lower values of the Frisch elasticity (more in line with microeconometric estimates) the gains are relatively small, but for more elastic labor supplies (more in agreement with the business cycle literature) the gains can be very large.

Testing the incentive effects in tournaments with a superstar

This paper studies the effects of the levels and the structure of prizes on the efforts of agents with heterogeneous ability in a tournament model. In particular, we examine how the presence of a highly able agent affects the effort levels of other agents as well as the effects of the total and the marginal prizes. Using panel data from the Japan Golf Tour, we estimate the effects of the presence of a superstar, and the size of the total and marginal prizes on the scores of professional golfers. We find that the presence of a superstar adversely affects the scores of the other players; that the larger the size of the total prize, the better are the scores; and that the larger the marginal prizes that players face at the end of the third round, the better the scores they achieve in the final round.     

Queueing problems with two parallel servers

Agents are waiting for their jobs to be processed at a service facility. All agents need the same processing time but have different waiting costs per unit of time. The facility has two parallel servers and can serve two agents at a time. We are interested in finding the order in which to serve agents and the (positive or negative) monetary transfers they should receive. We introduce two rules, the "minimal transfer rule" and the "maximal transfer rule". We show that they correspond to the Shapley (1953) values of associated queueing games, for two alternative definitions of the worth of a coalition. The two-server queueing games correspond to the games similarly defined by Maniquet (2003) and Chun (2006a) for one server. If the worth of a coalition is defined by assuming that the coalitional members are served before the non-coalitional members, then the minimal transfer rule is obtained. If it is defined by assuming that the coalitional members are served after the non-coalitional members, then the maximal transfer rule is obtained.     

Gender Differences in the Giving and Taking Variants of the Dictator Game

We run between‐subject dictator games with exogenously specified “give” or “take” frames involving a balanced pool of male and female dictators and constant payoff possibilities. We find the following: Females allocate more under the taking frame than under the giving frame. Males allocate more under the giving frame than under the taking frame. In the taking frame females are more generous than males. But in the giving frame both are equally generous. Finally, when the combined population of males and females is considered, giving is found to be equivalent to “not taking,” because the opposing gender effects offset each other.     

Nash equilibria of games when players’ preferences are quasi‐transitive

Much of game theory is founded on the assumption that individual players are endowed with preferences that can be represented by a real‐valued utility function. However, in reality human preferences are often not transitive. This is especially true for the indifference relation, which can lead an individual to make a series of choices which in their totality would be viewed by the same individual as erroneous. There is a substantial literature that raises intricate questions about individual liberty and the role of government intervention in such contexts. The aim of this paper is not to go into these ethical matters but to provide a formal structure for such analysis by characterizing games where individual preferences are quasi‐transitive. The paper identifies a set of axioms which are sufficient for the existence of Nash equilibria in such “games.”     

Why factors facilitating collusion may not predict cartel occurrence — experimental evidence

Factors facilitating collusion may not successfully predict cartel occurrence: When a factor predicts that collusion (explicit and tacit) becomes easier, firms might be less inclined to set up a cartel simply because tacit coordination already tends to go in hand with supra-competitive profits. We illustrate this issue with laboratory data. We run n-firm Cournot experiments with written cheap-talk communication between players and we compare them to treatments without the possibility to talk. We conduct this comparison for two, four, and six firms. We find that two firms indeed find it easier to collude tacitly but that the number of firms does not significantly affect outcomes with communication. As a result, the payoff gain from communication increases with the number of firms, at a decreasing rate.     

Managing Insurance Company Financial Statements to Meet Regulatory and Tax Reporting Goals*

This study investigates the extent to which property-casualty insurers select levels of loss reserves, net capital gains, and net stock transactions to meet solvency and tax reporting goals. Insurer solvency is reflected in financial measures known as IRIS (Insurance Regulatory Information System) ratios. IRIS ratios are generally enhanced by underestimating loss reserves, accelerating the realization of capital gains, postponing the realization of capital losses, issuing stock, and cutting dividends. Taxable income is reduced by reporting higher reserves and lower net capital gains on investments. We use simultaneous equations to model the three discretionary choices individually, while controlling for potential tradeoffs among the decisions. During the sample period of the study (1990-95), there is a shift in the regulatory environment that we argue tends to reduce incentives to meet IRIS goals. Specifically, risk-based capital (RBC) requirements were adopted in 1994. Although IRIS ratios continued to be used for solvency screening, their effect is expected to be diluted in the post-RBC period. Our results provide qualified support for this claim. Evidence of the phenomenon is stronger when the choice variables are net capital gains and stock transactions, and weaker when loss reserves are considered. Two of the three discretionary choices affect taxable income: loss reserves and capital gains. We find that tax incentives are significantly associated with the loss reserve estimate throughout the sample period. In contrast, our results are only weakly consistent with the view that capital gains are timed to achieve tax relief.     

Synergy among Seemingly Independent Activities*

“Synergy” implies that the value of activities undertaken jointly is greater than the sum of the values of the individual activities. Reasons cited for synergy include economies of scale, benefits due to vertical integration, and efficiency gains from shared inputs and skills. This paper shows that incentive (control) reasons alone can make activities synergistic. The result is derived in a model of adverse selection with risk‐neutral participants and linear technology. The linearity in the setting removes any obvious benefits to undertaking activities in tandem. Synergy gains are attributed to a convexity in the principal's payoff introduced by the activities' impact on the production versus rents trade‐off.