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Abstract:
We present a non-technical account of ambiguity in strategic games and show how it may be applied to economics and social sciences. Optimistic and pessimistic responses to ambiguity are formally modelled. We show that pessimism has the effect of increasing (decreasing) equilibrium prices under Cournot (Bertrand) competition. In addition the effects of ambiguity on peace-making are examined. It is shown that ambiguity may select equilibria in coordination games with multiple equilibria. Some comparative statics results are derived for the impact of ambiguity in games with strategic complements.

Ambiguity, Optimism, Pessimism, Oligopoly, Strategic Delegation, Peace-making, Choquet expected utility

Abstract:
Recently there has been much work on learning in games. However, learning usually means learning about behavior of opponents rather than learning about the game as such. Here we test in an experiment whether players in a repeated encounter can learn the payoff structures of their opponents by rewarding subjects for correct guesses. Our data allows to construct the games that subjects perceive to be playing, the subjective games. We find that subjects often play according to an equilibrium in their subjective game. However, subjective games frequently differ from the games actually played.

learning, subjective games, experiments

Abstract:
Recently there has been much work on learning in games. However, learning usually means "learning about behavior of opponents" rather than "learning about the game" as such. Here we test in an experiment whether players in a repeated encounter can learn the payoff structures of their opponents by rewarding subjects for correct guesses. Our data allows to construct the games that subjects perceive to be playing, the subjective games. We find that subjects often play according to an equilibrium in their subjective game. However, subjective games frequently differ from the games actually played.

learning, subjective games, experiments

Abstract:
The standard state-spaces of asymmetric information preclude non-trivial forms of unawareness (Modica and Rustichini, 1994, Dekel, Lipman and Rustichini, 1998). We introduce a generalized state-space model that allows for non-trivial unawareness among several individuals, and which satisfies strong properties of knowledge as well as all the desiderata on unawareness proposed this far in the literature.

unawareness, awareness, knowledge, interactive epistemology, speculative trade, bounded perception

Abstract:
We present a formal model of symmetric n-firm Cournot oligopoly with a heterogeneous population of optimizers and imitators. Imitators mimic the output decision of the most successful firms of the previous round a la Vega-Redondo (1997). Optimizers play a myopic best response to the opponents' previous output. The dynamics of the decision rules induce a Markov chain. As expression of bounded rationality, firms are allowed to make mistakes and deviate from the decision rules with a small probability. Applying stochastic stability analysis, we find that the long run distribution converges to a recurrent set of states in which imitators are better off than are optimizers. This finding appears to be robust even when optimizers are more sophisticated. It suggests that imitators drive optimizers out of the market contradicting a fundamental conjecture by Friedman (1953).

profit maximization hypothesis, bounded rationality, learning, Stackelberg

Abstract:
In the economic literature on market competition, firms are often modelled as individual decision makers and the internal organization of the firm is neglected (unitary player assumption). However, as the literature on strategic delegation suggests, one can not generally expect that the behavior of teams is equivalent to the behavior of individuals in Cournot competition. Nevertheless, there are models of team-organization such that team-firms and individual firms are behaviorally equivalent. This provides a theoretical foundation for the unitary player assumption in Cournot competition. We show that this assumption is robust in experiments, which is in contrast to experimental results on price competition.

Unitary player assumption, experiments, group behavior, theory of the firm

Abstract:
Heifetz, Meier and Schipper (2006) introduced unawareness structures. These are generalized state-space models that allow for non-trivial unawareness among several individuals and strong properties of knowledge. We show that a canonical unawareness structure arises naturally if states consist of maximally consistent sets of formulas in an appropriate axiom system. As a corollary, we obtain a strong soundness and completeness theorem for this axiom system with respect to the class of unawareness structures.

Unawareness, awareness, knowledge, interactive epistemology, modal logic, lack of conception, bounded perception

Abstract:
Vega-Redondo (1997) showed that imitation leads to the Walrasian outcome in Cournot Oligopoly. We generalize his result to aggregative quasi-submodular games. Examples are the Cournot Oligopoly, Bertrand games with differentiated complementary products, Common-Pool Resource games, Rent-Seeking games and generalized Nash-Demand games.

Imitation, aggregate-taking strategy, price-taking behavior, stochastic stability

Abstract:
Vega-Redondo (1997) showed that imitation leads to the Walrasian outcome in Cournot Oligopoly. We generalize his result to aggregative quasi-submodular games. Examples are the Cournot Oligopoly, Bertrand games with differentiated complementary products, Common-Pool Resource games, Rent-Seeking games and generalized Nash-Demand games.

imitation, price-taking behavior, lattice theory, stochastic stability

Abstract:
Neuroeconomics focuses on brain imaging studies mapping neural responses to choice behavior. Economic theory is concerned with choice behavior but it is silent on neural activities. We present a game theoretic model in which players are endowed with an additional structure - a simple nervous system - and interact repeatedly in changing games. The nervous system constrains information processing functions and behavioral functions. By reinterpreting results from evolutionary game theory (Germano, 2007), we suggest that nervous systems can develop to function well in exogenously changing strategic environments. We present an example indicating that an analogous conclusion fails if players can influence endogenously their environment.

Neuroeconomic theory, Evolutionary game theory, Learning in games

Abstract:
We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for many potential applications of asymmetric unawareness. We develop Bayesian games with unawareness, define equilibrium, and prove existence. We show how equilibria are extended naturally from lower to higher awareness levels and restricted from higher to lower awareness levels. We use our unawareness belief structure to show that the common prior assumption is too weak to rule out speculative trade in all states. Yet, we prove a generalized "No-trade" theorem according to which there can not be common certainty of strict preference to trade. Moreover, we show a generalization of the "No-agreeing-to-disagree" theorem.

unawareness, awareness, type-space, Bayesian games, incomplete information, equilibrium, common prior, agreement, speculative trade, interactive epistemology

Abstract:
Contrary to claims by Gul and Pesendorfer (2008), I show that standard economics makes use of non-choice evidence in a meaningful way. This is because standard economics solely grounded in the theory of choice is "incomplete''. That is, it has content that can not be revealed with any general choice procedure.

Revealed preference, theory of choice, neuroeconomics, non-choice evidence, machines

Abstract:
We use an experiment to explore how subjects learn to play against computers which are programmed to follow one of a number of standard learning algorithms. The learning theories are (unbeknown to subjects) a best response process, fictitious play, imitation, reinforcement learning, and a trial & error process. We test whether subjects try to influence those algorithms to their advantage in a forward-looking way (strategic teaching). We find that strategic teaching occurs frequently and that all learning algorithms are subject to exploitation with the notable exception of imitation. The experiment was conducted, both, on the internet and in the usual laboratory setting. We find some systematic differences, which however can be traced to the different incentives structures rather than the experimental environment.

learning, fictitious play, imitation, reinforcement, trial & error, strategic teaching, Cournot duopoly, experiments, internet

Abstract:
We report on an experiment in which subjects choose actions in strategic games with either strategic complements or substitutes against a granny, a game theorist or other subjects. The games are selected in order to test predictions on the comparative statics of equilibrium with respect to changes in strategic ambiguity. We find that subjects face higher ambiguity while playing against the granny than playing against the game theorist if we assume that subjects are ambiguity averse. Moreover, under the same assumption, subjects choose more secure actions in games more prone to ambiguity which is in line with the predictions.

Knightian uncertainty, Choquet expected utility, equilibrium under ambiguity, strategic uncertainty, experiments

Abstract:
We define generalized extensive-form games which allow for mutual unawareness of actions. We extend Pearce's (1984) notion of extensive-form (correlated) rationalizability to this setting, explore its properties and prove existence. We define also a new variant of this solution concept, prudent rationalizability, which refines the set of outcomes induced by extensive-form rationalizable strategies. We apply prudent rationalizability to the analysis of verifiable communication with unawareness. Finally, we define the normal form of a generalized extensive-form game, and characterize in it extensive-form rationalizability by iterative conditional dominance.

Unawareness, extensive-form games, extensive-form rationalizability, prudent rationalizability, iterative conditional dominance

Abstract:
In an experiment using two-bidder first-price sealed bid auctions with symmetric independent private values, we scan also the right hand of each subject. We study how the ratio of the length of the index and ring fingers (2D:4D) of the right hand, a measure of prenatal hormone exposure, is correlated with bidding behavior and total profits. 2D:4D has been reported to predict competitiveness in sports competition (Manning and Taylor, 2001, and Honekopp, Manning and Muller, 2006), risk aversion in an investment task (Dreber and Hoffman, 2007), and the average profitability of high-frequency traders in financial markets (Coates, Gurnell and Rustichini, 2009). We do not find any significant correlation between 2D:4D and both bidding or profits. Yet, our study raises an issue of ethnic differences with respect to 2D:4D.

Hormones, Digit ratio, 2D:4D, Risk behavior, Competition, Competitive behavior, Bidding, Endocrinological economics

Abstract:
In an experiment using two-bidder first-price sealed bid auctions with symmetric independent private values, we collected information on the female participants' menstrual cycles. We find that women bid significantly higher than men in their menstrual and premenstrual phase but do not bid significantly different in other phases of the menstrual cycle. We suggest an evolutionary hypothesis according to which women are genetically predisposed by hormones to generally behave more riskily during their fertile phase of their menstrual cycle in order to increase the probability of conception, quality of offspring, and genetic variety. Our finding is in contrast to results by Chen, Katuscak and Ozdenoren (2005, 2009).

Hormones, Menstrual cycle, Gender, Likelihood of conception, First price auction, Risk behavior, Competition, Bidding, Endocrinological economics

Abstract:
We define a generalized state-space model with interactive unawareness and probabilistic beliefs. Such models are desirable for potential applications of asymmetric unawareness. We compare unawareness with probability zero belief. Applying our unawareness belief structures, we show that the common prior assumption is too weak to rule out speculative trade in all states. Yet, we prove a generalized "No-trade" theorem according to which there can not be common certainty of strict preference to trade. Moreover, we show a generalization of the "No-agreeing-to-disagree" theorem.

Unawareness, awareness, zero probability, type-space, common prior, agreement, speculative trade, interactive epistemology

Abstract:
A decision-maker is said to have an ambiguous belief if it is not precise enough to be represented by a single probability distribution. The pervasive assumption in game theoretic models in economics is that players' beliefs are unambiguous. This paper argues, drawing on examples from economics and politics, that it may be illuminating, in instances, to model players as having ambiguous beliefs. Optimistic and pessimistic responses to ambiguity are formally modelled. We show that pessimism has the effect of increasing (decreasing) equilibrium prices under Cournot (Bertrand) competition. In addition the effects of ambiguity on peace-making are examined. It is shown that ambiguity may select equilibria in coordination games with multiple equilibria. Some comparative statics results are derived for the impact of ambiguity in games with strategic complements.