Elias Tsakas

The target projection dynamic

We study the target projection dynamic, a model of learning in normal form games. The dynamic is given a microeconomic foundation in terms of myopic optimization under control costs due to a certain status-quo bias. We establish a number of desirable properties of the dynamic: existence, uniqueness and continuity of solution trajectories, Nash stationarity, positive correlation with payoffs, and innovation. Sufficient conditions are provided under which strictly dominated strategies are wiped out. Finally, some stability results are provided for special classes of games.

Pairwise epistemic conditions for Nash equilibrium

We introduce a framework for modeling pairwise interactive beliefs and provide an epistemic foundation for Nash equilibrium in terms of pairwise epistemic conditions locally imposed on only some pairs of players. Our main result considerably weakens not only the standard sufficient conditions by Aumann and Brandenburger (1995), but also the subsequent generalization by Barelli (2009). Surprisingly, our conditions do not require nor imply mutual belief in rationality.

Growth and Inequality in Public Good Games

In a novel experimental design we study dynamic public good games in which wealth is allowed to accumulate. More precisely each agents income at the end of a period serves as her endowment in the following period. In this setting growth and inequality arise endogenously allowing us to address new questions regarding their interplay and effect on cooperation levels. We find that average cooperation levels in this setting are high (between 20-60% of endowments) and that amounts contributed do not decline over time. Introducing the possibility of punishment leads to lower group income, but less inequality within groups. In both treatments (with and w/o punishment) inequality and group income are positively correlated for poor groups (with below median income), but negatively correlated for rich groups (with above median income). There is very strong path dependence: inequality in early periods is strongly negatively correlated with group income in later periods. These results give new insights into why people cooperate and should make us rethink previous results from the literature on repeated public good games regarding the decay of cooperation in the absence of punishment.

Epistemic equivalence of extended belief hierarchies

In this paper, we introduce a notion of epistemic equivalence between hierarchies of conditional beliefs and hierarchies of lexicographic beliefs, thus extending the standard equivalence results of Halpern (2010) and Brandenburger et al. (2007) to an interactive setting, and we show that there is a Borel surjective function, mapping each conditional belief hierarchy to its epistemically equivalent lexicographic belief hierarchy. Then, using our equivalence result we construct a terminal type space model for lexicographic belief hierarchies. Finally, we show that whenever we restrict attention to full-support beliefs, epistemic equivalence between a lexicographic belief hierarchy and a conditional belief hierarchy implies that an arbitrary Borel event is commonly assumed under the lexicographic belief hierarchy if and only if it is commonly strongly believed under the conditional belief hierarchy. This is the first result in the literature directly linking common assumption in rationality (Brandenburger et al., 2008) with common strong belief in rationality (Battigalli and Siniscalchi, 2002).

Correlated-belief equilibrium

We introduce a new solution concept, called correlated-belief equilibrium. The difference to Nash equilibrium is that, while each player has correct marginal conjectures about each opponent, it is not necessarily the case that these marginal conjectures are independent. Then, we provide an epistemic foundation and we relate correlated-belief equilibrium with standard solution concepts, such as rationalizability, correlated equilibrium and conjectural equilibrium.

UNIVERSALLY RATIONAL BELIEF HIERARCHIES

In a recent paper, Tsakas [2013 Rational belief hierarchies, Journal of Mathematical Economics, Maastricht University] introduced the notion of rational beliefs. These are Borel probability measures that assign a rational probability to every Borel event. Then, he constructed the corresponding Harsanyi type space model that represents the rational belief hierarchies. As he showed, there are rational types that are associated with a non-rational probability measure over the product of the underlying space of uncertainty and the opponents types. In this paper, we define the universally rational belief hierarchies, as those that do not exhibit this property. Then, we characterize them in terms of a natural restriction imposed directly on the belief hierarchies.

On consensus through communication without a commonly known protocol

The present paper extends the standard model of pairwise communication among Bayesianagents to cases where the structure of the communication protocol is not commonly known.We show that, even under strict conditions on the structure of the protocols and the nature of the transmitted signals, a consensus may never be reached if very little asymmetric information about the protocol is introduced.

Common belief in approximate rationality

Abstract This paper substitutes the standard rationality assumption with approximate rationality in normal form games. We assume that players believe that their opponents might be e -rational, i.e. willing to settle for a suboptimal choice, and so give up an amount e of expected utility, in response to the belief they hold. For every player i and every opponents’ degree of rationality e , we require player i to attach at least probability F i ( e ) to his opponent being e -rational, where the functions F i are assumed to be common knowledge amongst the players. We refer to this event as belief in F -rationality. The notion of Common Belief in F -Rationality (CB F R) is then introduced as an approximate rationality counterpart of the established Common Belief in Rationality. Finally, a corresponding recursive procedure is designed that characterizes those beliefs players can hold under CB F R.

Limited focus in dynamic games

In this paper we introduce a novel framework that allows us to model games with players who reason about the opponents’ rationality only in some part of the game tree. We refer to this type of bounded rationality as limited focus. In particular, players try to rationalize their opponents’ moves only at the histories they focus on, i.e., formally, they strongly believe in their opponents’ rationality in these particular histories only. Our main result characterizes the strategy profiles that can be played under rationality and common strong belief in rationality by means of a simple elimination procedure, for every specification of the players’ focus. Finally, we present several special cases and applications of our framework, and we discuss how it differs from other forms of bounded perception such as unawareness.

Common belief of weak-dominance rationality in strategic-form games: A qualitative analysis

Abstract We study common belief of weak-dominance rationality in strategic-form games with ordinal utilities, employing a qualitative model of beliefs. We characterize two standard solution concepts for such games: the Iterated Deletion of Borgers-dominated Strategies (IDBS) and the Iterated Deletion of Inferior Strategy Profiles (IDIP). We do so by imposing nested restrictions on the doxastic models: namely, the respective epistemic conditions differ in the fact that IDIP requires the truth axiom whereas IDBS does not. Hence, IDIP refines IDBS.