Hyun Song Shin

Approximate Common Knowledge and Co-ordination: Recent Lessons from Game Theory

The importance of the notion of common knowledge in sustaining cooperative outcomes in strategic situations is well appreciated. However, the systematic analysis of the extent to which small departures from common knowledge affect equilibrium in games has only recently been attempted.We review the main themes in this literature, in particular, the notion of common p-belief. We outline both the analytical issues raised, and the potential applicability of such ideas to game theory, computer science and the philosophy of language.

Comparing the Robustness of Trading Systems to Higher Order Uncertainty

This paper compares the performance of a decentralized market with that of a dealership market when traders have differential information. Trade occurs as a result of equilibrium actions in a Bayesian game, where uncertainty is captured by a finite state space and information is represented by partitions on this space. In the benchmark case of trade with common knowledge of endowments, the two mechanisms deliver virtually identical outcomes. However, with differential information, the dealership market has strictly higher trading volume, and yields an efficient post-trade allocation in most states. In contrast, the decentralized market suffers from suboptimal trading volume. The reason for this poor performance is the vulnerability of the decentralized market to higher-order uncertainty concerning the fundamentals of the market. Traders may know that mutually beneficial trade is feasible, and perhaps know that they know, and yet a failure of common knowledge that this is so precludes efficient trade. The dealership market is robust to this type of uncertainty.

A violation of dominance and the consumption value of gambling

We document an apparently widespread violation of dominance in the horse-racing betting market in the UK, and use the systematic variation in the incidence of this violation to estimate the consumption value of gambling. Betting-shop gamblers in the UK face a tax on gambling of 10%, but have the choice of paying the tax either at the time of wager or on any return on a successful bet. It can be shown, however, that the latter act is strictly dominated by another action in which tax is paid on the wager. Despite this, more than 18% of bets appear to be placed by gamblers who choose to pay tax on the return. We explore the hypothesis that this apparent violation of rationality may be explained by a component of utility which represents the consumption value of gambling, which in turn varies with the amount wagered. We then estimate this component from a dataset consisting of a record of 25,000 individual bets using probit analysis of the tax decision.

Representing the knowledge of turing machines

When each state of the world is a maximally specific, consistent description of the world, including the description of the knowledge and ignorance of all individuals, the standard partitional model of knowledge is inconsistent with the assumption that an individuals powers are limited to that of a Turing machine. We show, however, that the epistemic logicS4 is consistent with computational constraints.

A reconstruction of Jeffrey's notion of ratifiability in terms of counterfactual beliefs

We formalize Jeffreys (1983) notion of ratifiability and show that the resulting formal structure can be obtained more directly by means of a theory of counterfactual beliefs. One implication is that, under the appropriate formalizations, together with certain restrictions on beliefs, Bayesian decision theory and causal decision theory coincide.

The rationality and efficacy of decisions under uncertainty and the value of an experiment

SummaryA decision maker faces a known prior distribution over payoff relevant states. We compare the expected utility of this individual under two scenarios. In the first, the decision maker makes a choice without further information. In the second, the decision maker has access to an experiment before choosing an action. However, the decision maker does not know the true joint distribution over states and messages. The value of the experiment as measured by the difference in the two utility levels can be negative as well as positive. We give a condition which is necessary and sufficient for the experiment to be valuable in our sense, for any decision problem.