This paper shows how minimax regret sheds new light on an old economic topic, market-exit games. It focuses wars of attrition, namely overcrowded duopoly markets where the strategic variable is exit time. The only symmetric Nash equilibrium (NE) game studied a mixed-strategy that leads to null expected payoff, i.e., payoff firm gets when it immediately exits market. result not convincing, both ...

We obtain minimax lower bounds on the regret for the classical two-armed bandit problem. We provide a nite-sample minimax version of the well-known log n asymptotic lower bound of Lai and Robbins. Also, in contrast to the logn asymptotic results on the regret, we show that the minimax regret is achieved by mere random guessing under fairly mild conditions on the set of allowable con gurations o...

In many areas of Artificial Intelligence (AI), we are interested in helping people make better decisions. This help can result in two advantages. First, computers can process large amounts of data and perform quick calculations, leading to better decisions. Second, if a user does not have to think about some decisions, they have more time to focus on other things they find important. Since user...

We obtain minimax lower bounds on the regret for the classical two-armed bandit problem. We provide a finite-sample minimax version of the well-known log asymptotic lower bound of Lai and Robbins. The finite-time lower bound allows us to derive conditions for the amount of time necessary to make any significant gain over a random guessing strategy. These bounds depend on the class of possible d...

In a partial monitoring game, the learner repeatedly chooses an action, the environment responds with an outcome, and then the learner suffers a loss and receives a feedback signal, both of which are fixed functions of the action and the outcome. The goal of the learner is to minimize his regret, which is the difference between his total cumulative loss and the total loss of the best fixed acti...

This note studies the problem of implementing social choice correspondences in environments where individuals have doubts about the rationality of their opponents. We postulate the concept of ε-minimax regret as our solution concept and show that social choice correspondences that are Maskin monotonic and satisfy the no-veto power condition are implementable in ε-minimax regret equilibrium

We study a strategic facility location problem under uncertainty. The uncertainty associated with future events is modeled by defining alternative future scenarios with probabilities. We present a new model which minimizes the expected regret with respect to an endogenously selected subset of worst-case scenarios whose collective probability of occurrence is exactly 1-α. We demonstrate the effe...

Sequential randomized prediction of an arbitrary binary sequence is investigated. No assumption is made on the mechanism of generating the bit sequence. The goal of the predictor is to minimize its relative loss (or regret), i.e., to make almost as few mistakes as the best “expert” in a fixed, possibly infinite, set of experts. We point out a surprising connection between this prediction proble...

This paper studies a variety of forms of regret minimization as the criteria with which traders choose their bids/asks in a double auction. Unlike the expected utility maximizers that populate typical market models, these traders do not determine their actions using a single prior. The analysis proves that minimax regret traders will not converge to price-taking as the number of traders in the ...

The precise specification of reward functions for Markov decision processes (MDPs) is often extremely difficult, motivating research into both reward elicitation and the robust solution of MDPs with imprecisely specified reward (IRMDPs). We develop new techniques for the robust optimization of IRMDPs, using the minimax regret decision criterion, that exploit the set of nondominated policies, i....