Bradley Conditionals and Dynamic Choice

One of the main contributions of Richard Bradley’s book is an elegant extension of Jeffrey’s Logic of Decision that countenances the evaluation of conditional prospects. This extension offers a promising new setting in which to model dynamic choice. In Bradley’s framework, plans can be understood as conditionals of an appropriate sort, while dynamic consistency can be viewed as providing a constraint on the evaluation of conditionals across time. In this paper, we study connections between planning conditionals and dynamic consistency.

Multiple Beliefs, Dominance and Dynamic Consistency

This paper investigates multiperiod decisions under multiple beliefs. We explore the dynamic consistency of both complete and incomplete orderings. We focus on a dominance concept that supports decision-making under multiple characterizations of uncertainty by ruling out strategies that are dominated across a set of beliefs. We uncover a distinction between two types of dynamic inconsistency, which we label fallacious and fallible inconsistency. Fallacious inconsistency occurs when an a priori optimal strategy is suboptimal in the second period, thus requiring the decision-maker to depart from the original strategy. Fallible inconsistency occurs when an a priori suboptimal second-period action ceases being suboptimal from the perspective of the second-period preferences. We introduce corresponding definitions of dynamic consistency and show that the two types of consistency are equivalent for complete orderings, but differ for incomplete orderings. Subjective expected utility is dynamically consistent and non-expected-utility decision rules, such as minmax, are not. We show that the dominance relation over beliefs falls between these two: it is immune to the more severe fallacious inconsistency, but not to the less problematic fallible inconsistency. We illustrate the method and concepts using a numerical example addressing a focal, real-world problem of risk and ambiguity regarding climate change. This paper was accepted by Ilia Tsetlin, decision analysis.

Dynamic consistency, valuable information and subjective beliefs

Ambiguity sensitive preferences must fail either Consequentialism or Dynamic Consistency (DC), two properties that are compatible with subjective expected utility and Bayesian updating, while forming the basis of backward induction and dynamic programming. We examine the connection between these properties in a general environment of convex preferences over monetary acts and find that, far from being incompatible, they are connected in an economically meaningful way. In single-agent decision problems, positive value of information characterises one direction of DC. We propose a weakening of DC and show that one direction is equivalent to weakly valuable information, whereas the other characterises the Bayesian updating of the subjective beliefs which are revealed by trading behavior.

Stochastic model of network formation with asymmetric players

We propose a model of a network formation using the theory of stochastic games with random terminal time. Initially, the leader proposes a joint project in the form of a network to the players. Then, the players have the opportunities to form new links with each other to update the network proposed by the leader. Any player's payoff at any stage is determined by the network structure. It is also assumed that the formation of links proposed by the players is random. The duration of the game is also random. As a result of the players' actions and the implementation of the random steps of the Nature, a network is formed. We consider a cooperative approach to network formation, and we use the CIS-value as a cooperative solution. In this paper, a recurrent formula for its derivation in any cooperative subgame is obtained. The paper also investigates the dynamic consistency of CIS-value. The theoretical results are demonstrated by a numerical example.