Dynamic coordination with individual learning

We study coordination in dynamic global games with private learning. Players choose whether and when to invest irreversibly in a project whose success depends on its quality and the timing of investment. Players gradually learn about project quality. We identify conditions on temporal incentives under which, in sufficiently long games, players coordinate on investing whenever doing so is not dominated. Roughly speaking, this outcome occurs whenever players? payoffs are sufficiently tolerant of non-simultaneous coordination. We also identify conditions under which players coordinate on the risk-dominant action. We provide foundations for these results in terms of higher order beliefs.     

Resolving Indeterminacy in Coordination Games: A New Approach Applied to a Pay-as-you-go Pension Scheme

This paper shows that when players ignore what outcome will emerge because of the presence of multiple equilibria, they can coordinate their expectations by forming an initial belief based on the principle of indifference followed by a process of reasoning that updates this belief. Since this procedure describes a natural way to form beliefs under indeterminacy, it is reasonable for every agent to conjecture that all the others form their beliefs according to the same logic. Exactly the fact that agents are aware that they form their beliefs following the same procedure allows them to successfully coordinate their expectations.      

Ambiguous act equilibria

A game-theoretic framework that allows for explicitly randomized strategies is used to study the effect of ambiguity aversion on equilibrium outcomes. The notions of “independent strategies” as well as of “common priors” are amended to render them applicable to games in which players lack probabilistic sophistication. Within this framework the equilibrium predictions of two-player games with ambiguity-averse and with ambiguity-neutral players are observationally equivalent. This equivalence result does not extend to the case of games with more than two players. A translation of the concept of equilibrium in beliefs to the context of ambiguity aversion yields substantially different predictions – even for the case with just two players.     

The lifeboat problem

We study an all-pay contest with multiple identical prizes (“lifeboat seats”). Prizes are partitioned into subsets of prizes (“lifeboats”). Players play a two-stage game. First, each player chooses an element of the partition (“a lifeboat”). Then each player competes for a prize in the subset chosen (“a seat”). We characterize and compare the subgame perfect equilibria in which all players employ pure strategies or all players play identical mixed strategies in the first stage. The partitioning of prizes can lead to coordination failure when players employ nondegenerate mixed strategies. In these equilibria some rents are sheltered and rent dissipation is reduced.     

Self-referential thinking and equilibrium as states of mind in games: fMRI evidence

Sixteen subjects' brain activity were scanned using fMRI as they made choices, expressed beliefs, and expressed iterated 2nd-order beliefs (what they think others believe they will do) in eight games. Cingulate cortex and prefrontal areas (active in “theory of mind” and social reasoning) are differentially activated in making choices versus expressing beliefs. Forming self-referential 2nd-order beliefs about what others think you will do seems to be a mixture of processes used to make choices and form beliefs. In equilibrium, there is little difference in neural activity across choice and belief tasks; there is a purely neural definition of equilibrium as a “state of mind.” “Strategic IQ,” actual earnings from choices and accurate beliefs, is negatively correlated with activity in the insula, suggesting poor strategic thinkers are too self-focused, and is positively correlated with ventral striatal activity (suggesting that high IQ subjects are spending more mental energy predicting rewards).     

Coordination of strategic responses to security threats: Laboratory evidence

Laboratory experiments are used to evaluate the extent to which players in games can coordinate investments that diminish the probability of losses due to security breaches or terrorist attacks. In this environment, economically sensible investments may be foregone if their potential benefits are negated by failures to invest in security at other sites. The result is a coordination game with a desirable high-payoff, high-security equilibrium and an undesirable low-security equilibrium that may result if players do not expect others to invest in security. One unique feature of this coordination situation is that investment in security by one player generates a positive externality such that all other players’ expected payoffs are increased, regardless of those other players’ investment decisions. Coordination failures are pervasive in a baseline experiment with simultaneous decisions, but coordination is improved if players are allowed to move in an endogenously determined sequence. In addition, coordinated security investments are observed more often when the largest single security threat to individuals is preventable by their own decisions to invest in security. The security coordination game is a “potential game,” and the success of coordination on the more secure equilibrium is related to the notion of potential function maximization and basin of attraction.      

Trust and reciprocity: misunderstandings

We contest a reductive view of trust, quite diffused in economics, and in studies influenced by the Game-Theory framework: the idea that trust has necessarily to do with contexts requiring “reciprocation”; or that trust is trust in the other’s reciprocation. A multi-layer cognitive model of trust will be proposed. Trust is not conceived only as an attitude towards the other, implying different kinds of beliefs (evaluations, expectations, beliefs on the other”s motives, etc.), but also as a willingness to rely on others that makes us dependent and vulnerable to them, as well as a concrete act of reliance based on this. Not necessarily we trust people because they will be willing to reciprocate; and we do not necessarily reciprocate for reciprocating. Trust (even “genuine” trust) is based on a variety of motivations ascribed to others and makes prevail the adoption of our needs and goals: from “altruism” to “self-interest”, from reciprocation to norms or to affective reasons.     

INCOMPLETE INFORMATION GAMES WITH MULTIPLE PRIORS*

We present a model of incomplete information games, where each player is endowed with a set of priors. Upon arrival of private information, it is assumed that each player “updates” his set of priors to a set of posterior beliefs, and then evaluates his actions by the most pessimistic posterior beliefs. So each player's preferences may exhibit aversion to ambiguity or uncertainty. We define a couple of equilibrium concepts, establish existence results for them, and demonstrate by examples how players’ views on uncertainty about the environment affect the strategic outcomes.     

Team reasoning theory: an experimental analysis of common reason to believe and social distance

The aim of this paper is to study the role of the “common reason to believe” (Sugden in Philos Explor 16:165–181, 2003) and the reduction of social distance within the theory of team reasoning. The analysis draws on data collected through a Traveler’s Dilemma experiment. To study the role of the common reason to believe, players’ beliefs in their counterparts’ choices are elicited, and the correlation between the endorsement of team reasoning and beliefs is considered. The relation between social distance and team reasoning is analyzed by introducing a meeting between the two players after the game. We show that the common reason to believe appropriately explains the internal logic of team reasoning and that a reduction of social distance does not produce any statistically significant effect on the probability that team reasoning will be used.     

A theory of collusion with partial mutual understanding

Unlawful collusion is when firms have a mutual understanding to coordinate their behavior for the purpose of achieving a supracompetitive outcome. Given the legal focus on mutual beliefs, this paper explores the role of mutual beliefs in producing collusion. Focusing on price leadership, firms are assumed to commonly believe that price increases will be at least matched but lack any shared understanding about who will lead, when they will, and at what prices. Sufficient conditions are derived which ensure that supracompetitive prices emerge. However, price is bounded below the maximal equilibrium price.     

Stated beliefs versus inferred beliefs: A methodological inquiry and experimental test

Belief elicitation in game experiments may be problematic if it changes game play. We experimentally verify that belief elicitation can alter paths of play in a two-player repeated asymmetric matching pennies game. Importantly, this effect occurs only during early periods and only for players with strongly asymmetric payoffs, consistent with a cognitive/affective effect on priors that may serve as a substitute for experience. These effects occur with a common scoring rule elicitation procedure, but not with simpler (unmotivated) statements of expected choices of opponents. Scoring rule belief elicitation improves the goodness of fit of structural models of belief learning, and prior beliefs implied by such models are both stronger and more realistic when beliefs are elicited than when they are not. We also find that “inferred beliefs” (beliefs estimated from past observed actions of opponents) can predict observed actions better than the “stated beliefs” from scoring rule belief elicitation.     

Countering the Power of Vested Interests: Advancing Rationality in Public Decision-Making

Seemingly Pareto-improving reforms face more opposition than they should. In earlier work, I presented an explanation: voters correctly saw reforms as part of a long-term dynamic game, and they correctly saw how the reform affected outcomes (e.g., by affecting beliefs or coalition formation). Recent advances in behavioral economics derived from insights from sociology emphasize preference endogeneity, noting that beliefs are affected by those of others with whom one identifies and need not be consistent with rationality, as conventionally defined. Thus, individuals may have beliefs about the economic system that differ from those of economists. People may support policies which economists’ analyses suggest are contrary to their interests because they believe these policies advance their interests. Based on previous analyses of the causes of these seeming perversities, I show how economists can modify policy proposals in ways that enhance likelihood of support, e.g., with contingent provisions which are operative in the states of the world that economists know (believe) are unlikely to occur, but which enhance the wellbeing of individuals with such beliefs in those states. Those selling products that are adverse to one’s health have learned how to persuade customers to buy them. Likewise, politicians who are selling policies that are adverse to society’s wellbeing have learned how to market their ideas. Economists will similarly have to learn how to persuade citizens of the desirability of the evidence- and theory-based policies that they advocate.     

Estimating the effects of forward guidance in rational expectations models

Simulations of forward guidance in rational expectations models should be assessed using the “modest policy interventions” framework introduced by Eric Leeper and Tao Zha. That is, the estimated effects of a policy intervention should be considered reliable only if that intervention is unlikely to trigger a revision in private sector beliefs about the way that monetary policy will be conducted. I show how to constrain simulations of forward guidance to ensure that they are regarded as modest policy interventions and illustrate the technique using a medium-scale DSGE model estimated on US data. I find that many experiments that generate the large responses of macroeconomic variables deemed implausible by many economists – the so-called “forward guidance puzzle” – are not modest policy interventions. Those experiments should therefore be treated with caution, since they may prompt agents to believe that there has been a change in the monetary policy regime that is not accounted for within the model. More reliable results can be obtained by constraining the experiment to be a modest policy intervention. In the cases I study, the quantitative effects on macroeconomic variables are more plausible when this constraint is imposed.     

Calvin's Reformation in Geneva: Self and Social Signalling

As Weber ( 1904 ) recognized, Calvinistic beliefs about predestination may constitute a powerful incentive for good works; an individual wishes to receive assurances about her future prospects of salvation, and good works may provide a positive signal about such prospects. These beliefs can in turn create a social pressure to behave well, as good works can also signal to others that individuals belong to the “elect” and are therefore likely to behave well in social interactions. Moreover, the Consistory, an institution created by Calvin to monitor and publicize individuals' behavior, can allow for such social signalling. We analyze these self and social signalling incentives, and show how religions affect levels of cooperation and coordination.     

Valuations and dynamics of negotiations

This paper analyzes three‐party negotiations in the presence of externalities. We obtain a closed‐form solution for the Markov perfect equilibrium of a multilateral non‐cooperative bargaining model, yielding an equilibrium value and dynamics of negotiations that are supported by experimental studies. Players’ values are monotonically increasing (or decreasing) in the amount of negative (or positive) externalities that they impose on others. Moreover, players’ values are continuous and piecewise linear on the worth of bilateral coalitions, and are inextricably related to their negotiation strategies: the equilibrium value is the Nash bargaining solution when no bilateral coalitions form; the Shapley value when all bilateral coalitions form; or the nucleolus, when either one bilateral coalition among “natural partners” or two bilateral coalitions including a “pivotal player” form.     

Between-game rule learning in dissimilar symmetric normal-form games

Rule learning posits that decision makers, rather than choosing over actions, choose over behavioral rules with different levels of sophistication. Rules are reinforced over time based on their historically observed payoffs in a given game. Past works on rule learning have shown that when playing a single game over a number of rounds, players can learn to form sophisticated beliefs about others. Here we are interested in learning that occurs between games where the set of actions is not directly comparable from one game to the next. We study a sequence of ten thrice-played dissimilar games. Using experimental data, we find that our rule learning model captures the ability of players to learn to reason across games. However, this learning appears different from within-game rule learning as previously documented. The main adjustment in sophistication occurs by switching from non-belief-based strategies to belief-based strategies. The sophistication of the beliefs themselves increases only slightly over time.     

Unfair inequality,governance and individual beliefs

Unfair inequality arises when incentives are not fairly tied to effort or investment across the socio-economic spectrum. The actual limitations on economic activity from this failure may depend on whether people believe the system is unfair, and how well governing institutions safeguard fair-play. In this paper, I study whether unfair wealth inequality is correlated with beliefs about fairness, and whether good governance can be a substitute in belief formations for decreases in unfair inequality. I find a that people in countries with recent increases in unfair wealth inequality are less likely to believe that inequality is due to fair processes. This relationship holds when“fair” determinants of inequality include effort, as well as moral and meritocratic components. The relationship is strongest in countries with poor quality governance. In countries with high quality governance, people appear to be more tolerant of unfair inequality, as it is only weakly reflected in their beliefs about process fairness.     

Learning to alternate

The Individual Evolutionary Learning (IEL) model explains human subjects’ behavior in a wide range of repeated games which have unique Nash equilibria. Using a variation of ‘better response’ strategies, IEL agents quickly learn to play Nash equilibrium strategies and their dynamic behavior is like that of humans subjects. In this paper we study whether IEL can also explain behavior in games with gains from coordination. We focus on the simplest such game: the 2 person repeated Battle of Sexes game. In laboratory experiments, two patterns of behavior often emerge: players either converge rapidly to one of the stage game Nash equilibria and stay there or learn to coordinate their actions and alternate between the two Nash equilibria every other round. We show that IEL explains this behavior if the human subjects are truly in the dark and do not know or believe they know their opponent’s payoffs. To explain the behavior when agents are not in the dark, we need to modify the basic IEL model and allow some agents to begin with a good idea about how to play. We show that if the proportion of inspired agents with good ideas is chosen judiciously, the behavior of IEL agents looks remarkably similar to that of human subjects in laboratory experiments.     

Measuring Strategic Uncertainty in Coordination Games

This paper proposes a method to measure strategic uncertainty by eliciting certainty equivalents analogous to measuring risk attitudes in lotteries. We apply this method by conducting experiments on a class of one-shot coordination games with strategic complementarities and choices between simple lotteries and sure payoff alternatives, both framed in a similar way. Despite the multiplicity of equilibria in the coordination games, aggregate behaviour is fairly predictable. The pure or mixed Nash equilibria cannot describe subjects' behaviour. We present two global games with private information about monetary payoffs and about risk aversion. While previous literature treats the parameters of a global game as given, we estimate them and show that both models describe observed behaviour well. The global-game selection for vanishing noise of private signals offers a good recommendation for actual players, given the observed distribution of actions. We also deduce subjective beliefs and compare them with objective probabilities.