This award funds research in game theory. The research answers two questions: First, how robust is the finding that repeated play permits more cooperative equilibrium outcomes than does one-shot play? And second, how can the standard model of rational decision making be generalized to account for various ways that real behavior deviates from that model while retaining much of the model's parsimony and force?
Work on the first question builds on the large literature on repeated games. In the earliest work on this topic, such as the familiar prisoner's dilemma,each player observes the intended action of the others every period, so it is easy to tell if someone has cheated on an implicit agreement to cooperate. In many settings, though, players observe only imperfect signals of one another's actions. One classis example is a repeated partnership game, where the probability that the period' task is done well, or completed at all, depends on both the effort of the players and on random factors, and neither player directly observes the effort of the other. With typical parameters, the efficient arrangement is for both partners to work, but if the game is played a single time with an unfamiliar opponent, the equilibrium outcome is for the partners to act selfishly and shirk. Past work has shown that there can nevertheless be cooperative equilibria in these games if the players interact repeatedly and are sufficiently patient. Roughly speaking,in these equilibria the players cooperate so long as the track record of the partnership is sufficiently good; they have an incentive to do so because they know that a series of bad outcomes will lead to a breakdown of cooperation.
The PI analyzes two extensions of this idea. In the first, players do not know e.g. the productivity of effort, so that they do not know how likely a good outcome is even if both partners work. The research question is to determine whether and when the partners will still be able to use the 'shadow of the future' to cooperate even though initially the causes of the observed outcomes are initially unclear. In the second extension, players will observe a noisy signal of other players actions (such as group output so far) at privately known times. In this case when a player audits the current performance of the group he is uncertain of just when others last observed it and of what they saw, which typically makes it harder for players to coordinate on cooperative play. Once again, the focus will be on finding conditions that allow self-interested players to cooperate in their common interest.
As a counterpoint to these theoretical analyses, the investigator also conducts laboratory experiments on repeated games with noisy signals. A pilot study done shows that subjects can and do cooperate despite the increased complexity of the noisy environment; the project studies just what sorts of strategies subjects actually use and which strategies would be most successful.
The second project is based on the dual-self model of self-control, which gives a precise mathematical formalization of the idea that some observed individual decisions are the result of a within-subject game between a short-run impulsive self and a cooler, more rational long run self. The dual-self model has already been shown to provide a unified explanation of a range of empirical facts which had previously been explained with separate models, such as a desire for self-commitment (e.g. not buying Scotch for fear it will be consumed too quickly, or locking up savings in illiquid and hard-to-access securities), time-inconsistent choice (preferring $100 today to $110 tomorrow, but preferring $110 in 366 days to $100 in 365 days) and the Allais paradox of decision theory. The project will further expand the model to better fit the heterogeneity of real-world risk preferences, and to provide a unified treatment of small-stakes risk aversion and the decreasing marginal utility of winnings that is implicit in most experiments on social preferences. Preliminary work has calibrated the model to several data sets, the project will use the model to explore an even broader range of behavior.
The broader impacts of this award include important interdisciplinary contributions and training graduate students in a number of scientific disciplines. The project?s work spans several subfields of economics and also connects to other disciplines. It will help strengthen ties between economic theorists and experimenters interested in behavioral economics, between economists working on repeated games and their counterparts in mathematics, and between economists working on interactive learning and their counterparts in computer science. The grant will also provide support for graduate students doing research on related topics. Taking a longer term view, we are hopeful that the proposed research will enhance our understanding of how and when reciprocal altruism leads to cooperation; this is of fundamental importance in many branches of social science and is also a key issue in evolutionary biology.
The project's two focii were cooperation in repeated games and the implications of costly self-control in the "dual-self" model of the PI's past work. Cooperation via reciprocity is a key feature of many social and biological systems. And costly self control is of interest to psychologists as well as economists, and has motivated changes in government policy to provide "nudges" to help people act in their own intterest. The project's work on repeated games identified the conditions under which reciprocial altruism and cooperation in repeated games can be supported by equilibrium play even when the players observe only noisy signals of each other's intended actions (for example a partner who claims they tried their best but has a poor outcome) and in addition do not know the structure of the noise-generating process (how the probability of a poor outcome depends on effort). It also found that the usual repeated game analysis extends to some but not all cases where players observe each other's performance with a lag. The work on the dual-self model calibrated the model on data from several past experiments, showing that they were consistent with a fixed stable distribution of preference parameters, and demonstrated how the model explains data on interaction of risk and delay that does not fit alternative models of self control: For example, when subjects are asked to make "Allais paradox" type choices with the payments to be received at a future data, fewer of them make the paradoxical pair of choices. he project also extended the model to better account for the effect of varying the delay between decisions and rewards, and incorporated cognitive resources to model how continued exercise of self control leads to "ego depletion" and thus more sensitivity to temptation.
