Cooperation and non-halting strategies

This note is a response to an unpublished paper by Evans and Thomas (1998) of which we have recently become aware. Evans and Thomas (1998) take issue with a paper that we published some years back on 'Cooperation and Effective Computability' in repeated games (Anderlini and Sabourian 1995). In that paper we showed that it is only the cooperative equilibria of an infinitely repeated two-player common-interest game with no discounting that survive both the restriction that players' strategies must be computable, and appropriately computable trembles. Evans and Thomas (1998) assert that our results are seemingly not robust to changes in the set of computable strategies at the disposal of each player. In particular, they claim that our equilibrium selection result does not extend to the case in which players are allowed to choose strategies that halt on certain histories but do not halt on others. The purpose of this note is to show that the claim in Evans and Thomas (1998) is misleading. We present a modification of the set-up of our earlier paper in which the cooperative equilibria are selected when strategies that halt on certain histories and do not halt on others are allowed. Although extensive modifications are required, the proof of this extension of our earlier result runs along the same general line of argument as the original proof

Why did the bankers behave so badly?

It is widely believed that bankers played an important role in causing the financial crisis that began in August 2007. In this paper we demonstrate that the compensation system in the financial services industry which rewards perceived talents, rather than long-term performance, leads rational bankers to exhibit belief persistence, overconfidence and confirmation bias

Approachability with Discounting

We establish a version of Blackwell’s (1956) approachability result with discounting. Our main result shows that, for convex sets, our notion of approachability with discounting is equivalent to Blackwell’s (1956) approachability. Our proofs are based on a concentration result for probability measures and on the minmax theorem for two-person, zero-sum games

Rules and Mutation - A Theory of How Efficiency and Rawlsian Egalitarianism/Symmetry May Emerge

For any game, we provide a justification for why in the long-run outcomes are mostly both efficient and egalitarian/symmetric in the Rawlsian sense. We do this by constructing an adaptive dynamic framework with four features. First, agents select rules to implement actions. Second, rule selection satisfies some minimal payoff monotonicity: rules that do best are chosen with a positive probability. Third, in choosing rules agents are subject to "small" random mutation. Fourth mutation is payoff-dependent with agents mutating more when they do badly than when they do well. Our main result is: if the set of feasible rules R is sufficiently rich then outcomes that survive maximise the payoff of the player that does least well. We also show that if R is restricted to those that do best-reply on uniform histories then outcomes that survive are efficient and egalitarian amongst the set of minimum weak CURB sets. Finally, we consider long-run outcomes assuming mutation is payoff-independent; in contrast to our strong selection result above, in this case we show indeterminacy: any outcome can survive if R is sufficiently rich

Breaking the Brexit Impasse: Achieving a Fair, Legitimate and Democratic Outcome

Unanimity on the question of UK exit from the EU is not within reach, but this does not mean that the House of Commons or the population at large can not find a way out of the current Brexit impasse that is fair and legitimate. We discuss different voting procedures which satisfy some important principles of democracy and which can select the option that can win a majority against all other alternatives in a head-to-head majority vote. We argue that strategic considerations play an important role and we propose a procedure that works well and can help break the impasse when voters act strategically. The procedure requires (1) that all options with some minimum support are on the agenda, (2) that voting takes place in multiple rounds and (3) that in each round the alternative with the least support is eliminated until in the last round only two alternatives are left and the majority winner is selected. We discuss how this procedure can be modified to take into account that some voters may vote non-strategically and how it, in practice, could be used either in the House of Commons or in a new referendum.</jats:p

Herding in Quality Assessment: An Application to Organ Transplantation

There are many economic environments in which an object is offered sequentially to prospective buyers. It is often observed that once the object for sale is turned down by one or more agents, those that follow do the same. One explanation that has been p

Cooperation and non-halting strategies

This note is a response to an unpublished paper by Evans and Thomas (1998) of which we have recently become aware. Evans and Thomas (1998) take issue with a paper that we published some years back on 'Cooperation and Effective Computability' in repeated games (Anderlini and Sabourian 1995). In that paper we showed that it is only the cooperative equilibria of an infinitely repeated two-player common-interest game with no discounting that survive both the restriction that players' strategies must be computable, and appropriately computable trembles. Evans and Thomas (1998) assert that our results are seemingly not robust to changes in the set of computable strategies at the disposal of each player. In particular, they claim that our equilibrium selection result does not extend to the case in which players are allowed to choose strategies that halt on certain histories but do not halt on others. The purpose of this note is to show that the claim in Evans and Thomas (1998) is misleading. We present a modification of the set-up of our earlier paper in which the cooperative equilibria are selected when strategies that halt on certain histories and do not halt on others are allowed. Although extensive modifications are required, the proof of this extension of our earlier result runs along the same general line of argument as the original proo