Sowing Doubt Optimally in Two-Person Repeated Games

Consider a two-person repeated game, where one of the players, P1, can sow doubt, in the mind of his opponent, as to what P1's payoffs are. This results in a two-person repeated game with incomplete information. By sowing doubt, P1 can sometimes increase his minimal equilibrium payoff in the original game. We prove that this minimum is maximal when only one payoff matrix, the negative of the payoff matrix of the opponent, is added (the opponent thus believes that he might play a zero-sum game). We obtain two formulas for calculating this maximal minimum payoff. Journal of Economic Literature Classification Numbers: C7, D8.     

Coordination, “Magic,” and Reinforcement Learning in a Market Entry Game

Previous experimental studies have documented quick convergence to equilibrium play in market entry games with a large number of agents. The present study examines the effect of the available information in a 12-player game in an attempt to account for these findings. In line with the prediction of a simple reinforcement learning model (Roth and Erev, 1995,Games Econ. Behav.8, 164–212), quick convergence to equilibrium is observed even given minimal information (unknown payoff rule). However, in violation of the basic model, information concerning other players' payoff increases the number of entrants. The information effect can be described by a variant of the basic reinforcement learning model assuming that the additional information changes the player's reference point.Journal of Economic LiteratureClassification Number: C7, C92.     

Evolution and Mixed Strategies

Selten (1980, J. Theoret. Biol., 84, 93–101) showed that no mixed equilibria are evolutionarily stable when players can condition their strategies on their roles in a game. Alternatively, Harsanyi's (1973, Int. J. Game Theory, 2, 1–23) purification argument implies that all mixed equilibria are approximations of strict, and hence evolutionarily stable, equilibria of games with slightly perturbed payoffs. This paper reconciles these results: Approximations of mixed equilibria have high invasion barriers, and hence are likely to persist, when payoff perturbations are relatively important and role identification is relatively noisy. When payoff perturbations are unimportant and role identification is precise, approximations of mixed equilibria will have small invasion barriers and are unlikely to persist. Journal of Economic Literature Classification Numbers: C70, C78.     

Learning,non-equilibrium beliefs,and non-pecuniary payoffs in an experimental game

Summary. We present a parametric learning model of players' dynamic and possibly out-of-equilibrium beliefs about other players' preferences that also incorporates random utility (noise). We estimate the model using the data from the four-country ultimatum game experiments of Roth et al. (1991). We find evidence that in the US and in Israel, the estimated beliefs of proposers are stationary and out-of-equilibrium, that in Slovenia, they are in equilibrium, and that in Japan, they are out-of-equilibrium, change from period to period and move away from equilibrium over time. In Japan and in the US, the estimated proposers' beliefs are further away from the uniform prior than the estimated equilibrium beliefs. The results seem to provide support for a non-pecuniary payoff explanation in all countries. Received: May 16, 2000; revised version: December 15, 2001 RID="*" ID="*" We thank Alvin Roth for providing us with the data sets of Roth, Prasnikar, Okuno-Fujiwara, and Zamir (1991). We are very grateful to Vincent Crawford, Joel Sobel, and an anonymous referee for all their comments and feedback. We are also grateful to J?rg Borrmann, Bruno Broseta, Jimmy Chan, Liran Einav, Bernd Engelmann, Drew Fudenberg, Oscar Jorda, Muriel Niederle, Pedro Pereira, Georg Weizs?cker, and audiences at the California Institute of Technology, Harvard University, Universidade Nova de Lisboa, University of Nevada, Las Vegas, and at the European Summer Meetings of the Econometric Society in Lausanne for their comments. Costa-Gomes was affiliated with the Harvard Business School during part of his work on this project. The usual disclaimer applies. Correspondence to:M.A. Costa-Gomes and K.G. Zauner     

Subgame-perfect implementation of bargaining solutions

We study house allocation problems introduced by L. Shapley and H. Scarf (1974, J. Math. Econ.1, 23–28). We prove that a mechanism (a social choice function) is individually rational, anonymous, strategy-proof, and nonbossy (but not necessarily Pareto efficient) if and only if it is either the core mechanism or the no-trade mechanism, where the no-trade mechanism is the one that selects the initial allocation for each profile of preferences. This result confirms the intuition that even if we are willing to accept inefficiency, there exists no interesting strategy-proof mechanism other than the core mechanism. Journal of Economic Literature Classification Numbers: C71, C78, D71, D78, D89.     

From private to public common agency

This note establishes that two propositions in the theory of private common agency by Laussel and Le Breton (J. Econ. Theory 100 (2001) 93) extend to a larger class of games, in which each principal's gross monetary payoff does not depend exclusively on the quantities she receives. A new result is offered to demonstrate that Proposition 4.3 is robust to the introduction of negative externalities. An existing result is reinterpreted to show that Proposition 4.2 is robust to the introduction of positive externalities.     

The social cost problem,rights, and the (non)empty core

We revisit the “Coase theorem” through the lens of a cooperative game model which takes into account the assignment of rights among agents involved in a problem of social cost. We consider the case where one polluter interacts with many potential victims. Given an assignment or a mapping of rights, we represent a social cost problem by a cooperative game. A solution consists in a payoff vector. We introduce three properties for a mapping of rights. First, core compatibility indicates that the core of the associated cooperative games is nonempty. Second, Kaldor‐Hicks core compatibility indicates that there is a payoff vector in the core where victims are fully compensated for the damage once the negotiations are completed. Third, no veto power for a victim says that no victim has the power to veto an agreement signed by the rest of the society. We then demonstrate two main results. First, core compatibility is satisfied if and only if the rights are assigned either to the polluter or to the entire set of victims. Second, there is no mapping of rights satisfying Kaldor‐Hicks core compatibility and no veto power for a victim.     

Is There a Link Between Exchange Rate Pass-Through and the Monetary Regime: Evidence from Sub-Saharan Africa and Latin America

This paper investigates the relationship between the monetary regime: pegged, currency board, dollarization, and the exchange rate pass-through for a sample consisting of 15 Sub-Saharan Africa countries and 12 Latin American countries. The research findings about pass-through rates will shed light on the feasibility of a monetary union for Sub-Saharan Africa. The inclusion of the latter country group was deemed desirable to explore pass-through behavior in several monetary regime options not often used in Sub-Saharan Africa.

European Monetary Integration and Aggregate Relative Deprivation: The Dull Side of the Shiny Euro

Drawing on the premise that the integration of economies revises people's social space and their comparators, we quantify social stress by aggregate relative deprivation, ARD; we calculate the effect of monetary mergers on ARD; and we document the validity of the superadditivity property of ARD for successive adoptions of a common currency by European countries. One feature of monetary unification, which replaces diverse currencies with a common currency, is that it brings about a change in the comparison environment, expanding the reference space of individuals in a given country to encompass individuals from the joining countries. Overall, calculations regarding six enlargements of the Economic and Monetary Union between 1999 and 2011 reveal an increase of ARD on six occasions when we hold incomes constant, and on five when we take into consideration changes in incomes. In addition, we observe an uneven distribution of the costs and benefits from monetary integration among the participating countries when these costs and benefits are measured in terms of ARD.     

Putting a price tag on others’ perceptions of us

Standard economic theories assume that people are self-interested and their wellbeing solely dependent on their own material gains or losses. Unless they have an impact on monetary payoffs, the perceptions of anonymous individuals are irrelevant to people’s decision making. However, a large body of research in sociology and social psychology demonstrates that self-identity is developed through one’s understanding of how one is perceived by others. Using (Cooley’s, Human nature and the social order, 1964) concept of the “looking-glass self” as a framework, we evaluate experimentally whether or not people care about the imputed judgment of anonymous others arising from their imagination of their perceptions. We implemented variants of the Becker–DeGroot–Marschak mechanism to elicit the monetary value attached to the perceptions by participants. In one variant, only nonnegative bids were allowed, while in another, negative bids were allowed. We show that in an environment in which the perceptions of others are only conveyed to participants anonymously and privately, self-interested individuals exhibited strong negative perception avoidance even though the perceptions have no impact on their monetary payoff. The participants were willing to spend a significant amount in order to avoid confirming the supposedly negative perception. Thus, for them, ignorance was truly bliss. We also show that, in the absence of the audience effect, the fair-minded participants adopted a neutral attitude towards the perception of them as fair.     

On Perceptions of Fairness: The Role of Valuations, Outside Options, and Information in Ultimatum Bargaining Games

This study examines fairness perceptions in ultimatum bargaining games with asymmetric payoffs, outside options, and different information states. Fairness perceptions were dependent on treatment conditions. Specifically, when proposers had higher chip values, dollar offers were lower than when responders had higher chip values. When responders had an outside option, offers were higher and were rejected less often than when proposers had an outside option. However, a given offer was rejected more often when responders had an outside option. Therefore, similar to the first mover advantage, the “advantaged” or “entitled” player received a higher monetary payoff than they would otherwise. When there was complete information about payoff amounts (payoff conversion rates and outside options), rejections occurred more often, and given offer amounts were rejected more often than when there was incomplete information. When there was incomplete information, offers were higher in the initial rounds than in the final rounds. These results suggest that proposers made offers strategically, making offers that would not be rejected, rather than out of a concern for fairness.     

A stress test of fairness measures in models of social utility

Summary. Current social utility models posit fairness as a motive for certain types of strategic behavior. The models differ, however, with respect to how fairness is measured. Distribution models measure fairness in terms of relative payoff comparisons. Reciprocal-kindness models measure fairness in terms of gifts given and gifts received. Reference points play an important role in both measures, but the reference points in reciprocal-kindness models are conditioned on the actions available to players, whereas those in distributive models are not. Data from an ultimatum game experiment that stress tests the kindness measure is consistent with the distributive measure. Data from an experiment that stress tests the distributive measure is inconsistent with the distributive measure, but moves in the direction opposite that implied by the kindness measure. A measure that combines relative payoff comparisons with a reference point conditioned on feasible actions provides a first approximation to our data.Received: 12 August 2002, Revised: 27 November 2003, JEL Classification Numbers: C78, C91, D63. Correspondence to: Axel OckenfelsBolton gratefully acknowledges the support of the National Science Foundation. Ockenfels thanks Alvin Roth and the Harvard Business School for their generous hospitality, and the Deutsche Forschungsgemeinschaft for their support through the Emmy Noether-program. Both authors gratefully acknowledge the hospitality of the Making Choices project at the Center for Interdisciplinary Research, University of Bielefeld during the summer of 2000. We also thank an anonymous referee and seminar participants in Bielefeld, Boston, Columbus, Harvard, and Jena for helpful comments.     

The Choquet Bargaining Solutions

We axiomatically investigate the problem of rationalizing bargaining solutions by social welfare functions that are linear in every rank-ordered subset of Rⁿ₊ . Such functions, the so-called Choquet integrals, have been widely used in the theories of collective and individual choice. We refer to bargaining solutions that can be rationalized by Choquet integrals as Choquet bargaining solutions. Our main result is a complete characterization of Choquet bargaining solutions. As a corollary of our main result, we also obtain a characterization of the generalized Gini bargaining solutions introduced by Blackorby et al. (1994, Econometrica62, 1161–1178). Journal of Economic Literature Classification Numbers: D71, C78.     

Fundamentals, the exchange rate and prospects for the current and future EU enlargements: evidence from Bulgaria, Croatia, Romania and Turkey

We analyze the link between macroeconomic fundamentals and exchange rate dynamics in two new and two potential EU member states: Bulgaria, Romania, Croatia, and Turkey. Given the different institutional settings of the exchange rate market in the countries of interest, we follow two different modelling strategies. For Romania and Turkey, we evaluate possible exchange rate misalignments based on a monetary model of exchange rate determination. In the case of Bulgaria and Croatia, with currency board and narrow-band peg arrangements against the euro, we discuss possible exit strategies and quantitatively assess the effects of the peg arrangements by means of simulation.

Germany and Italy: conflicting policy paradigms towards European monetary integration?

In the literature on European monetary integration Germany and Italy are mostly strongly contrasted. However, this paper argues that there were important similarities between the policy paradigms in these two countries, in particular if a broader historical perspective is adopted. This work analyses the policy paradigms towards European monetary integration in Italy and Germany. Moreover, it contextualises these paradigms into the national institutional setting: while Germany was characterised by power sharing institutions, Italy featured power fragmentation (something which also affected the economic performance of both countries). There were significant differences between the policy paradigms of foreign policy-makers and economic policy-makers. Foreign policy makers, in both countries, under the influence of a European federalist vision, were strongly in favour of European monetary integration. These beliefs of foreign policy decision makers were crucial in charting EMU policy at history-making moments. The pro EMU policy paradigms of foreign policymakers contrasted, during most of the period covered, with the more sceptical beliefs of economic policy makers. In both countries, economic policy-makers, at different moments, had doubts whether enough “convergence” had been reached to make a more stable exchange rate system sustainable.

Uncertainty avoidance and the rate of business ownership across 21 OECD countries, 1976–2004

Persistent differences in the level of business ownership across countries have attracted the attention of scientific as well as political debate. Cultural as well as economic influences are assumed to play a role. This paper deals with the influence of cultural attitudes towards uncertainty on the rate of business ownership across 21 OECD countries. First, the concepts of uncertainty and risk are elaborated, as well as their relevance for entrepreneurship. An occupational choice model is introduced to underpin our reasoning at the macro-level. Second, regression analysis using pooled macro data for 1976, 1990 and 2004 and controlling for several economic variables, yields evidence that uncertainty avoidance is positively correlated with the prevalence of business ownership. According to our model, a restrictive climate of large organizations in high uncertainty avoidance countries pushes individuals striving for autonomy towards self-employment. Regressions for these 3 years separately show that in 2004, this positive correlation is no longer found, indicating that a compensating pull of entrepreneurship in countries with low uncertainty avoidance may have gained momentum in recent years. Third, an interaction term between uncertainty avoidance and GDP per capita in the pooled panel regressions shows that the historical negative relationship between GDP per capita and the level of business ownership is substantially weaker for countries with lower uncertainty avoidance. This suggests that rising opportunity costs of self-employment play a less important role in this cultural environment, or are being compensated by increasing entrepreneurial opportunities.

Minimum Memory for Equivalence between Ex Ante Optimality and Time-Consistency

I give a necessary and sufficient condition on memory of a player in an extensive game for equivalence between ex ante optimality and time-consistency (for all payoff assignments). The condition is called A-loss recall and requires that each loss of a player's memory can be traced back to some loss of memory of his own action. A-loss recall is also shown to be a necessary and sufficient condition for the existence of a time-consistent strategy (for all payoff assignments) if the player is conscious-minded. Journal of Economic Literature Classification Numbers: C72, D80.     

Debt Relief Incentives in Highly Indebted Poor Countries (HIPC): An Empirical Assessment

For more than two decades, the majority of countries in the African continent have experienced repeated episodes of rising external debt and debt service, which has led to numerous efforts of external debt relief. This paper provides new evidence on the effects of the Heavily Indebted Poor Countries (HIPC) Initiative on different economic and social indicators in 60 low income countries (LICs). Results show that LICs that were included in the HIPC Initiative marginally performed better than non-HIPC countries. There is evidence that countries that have reached the completion point of the HIPC Initiative by 2005 have experienced an average improvement in investment, health care, gross secondary education enrollment, and GDP per capita growth.

Payoff Assessments without Probabilities: A Simple Dynamic Model of Choice

We develop a model which reflects the tendency of people to simplify the decision problems they face. The decision maker chooses among alternate strategies only on the basis of the payoff she assesses she would obtain from them, and these assessments do not explicitly take into account her subjective judgements regarding the likelihood of alternate states of the world. At each stage, the decision maker chooses the strategy that she assesses to give the highest payoff. She updates her assessments adaptively. We show that such behavior leads to maxmin choices. We also consider the decision maker who experiences shocks. Journal of Economic Literature Classification Numbers: C7, D8.     

Experiment-inspired comments on John Roemer’s theory of cooperation

Abstract

We report on a nonsocial experiment where we find that all participants choose the dominant strategy in the experimental payoff, and compare it with the payoff-isomorphic, but social, Prisoner’s Dilemma treatment presented in a recent paper by Bosch-Domènech and Silvestre where 28% choose cooperation instead of the dominant strategy. The contrast reinforces Roemer’s emphasis on human cooperation. Next, we argue that Roemer’s Simple Kantian Equilibrium works well as a theory of cooperation under the assumption of monotonicity (positive or negative externalities), but not when efficient cooperation requires the division of labor by coordinating dissimilar tasks.