Randomization and simplification in dynamic decision-making

Randomization adds beneficial flexibility to the construction of optimal simple plans in dynamic environments. A decision-maker, restricted to the use of simple plans, may find a stochastic plan that strictly outperforms all deterministic ones. This is true even in noninteractive deterministic environments where the decision-maker's choices have no influence on his signals nor on the future evolution of the system. We describe a natural decomposition of simple plans into two components: an action selection rule and a behavior modification rule. In noninteractive environments optimal simple plans do not require randomization in the action selection rule. Only randomization in the behavior modification rule may be necessary.     

Justifiable preferences

We characterize preferences over acts that can be represented by a utility function and a multiple-prior, such that an act f is preferred to act g if there is a prior under which the expected utility induced by f is higher than that induced by g. These preferences are referred to as justifiable preferences. We further introduce a generalized model of ambiguity that involves a collection of multiple-priors, namely, multiple multiple-priors and incorporate Bewley?s Knightian model in justifiability: f is preferred to g if, according to at least one set of priors, f is unanimously preferred to g.     

The Scope of Anonymous Voluntary Bargaining Under Asymmetric Information

We present a model of anonymous collective bargaining where individuals'preferences and information may be significantly interdependent. We showthat the bargaining outcome becomes independent of individuals'preferences and information as the bargaining group increases in size. As acorollary, we show that anonymous voluntary bargaining completely fails inlarge groups. Either the difference between the bargaining outcome and thestatus quo vanishes as the size of the group becomes larger, or, thebargaining becomes coercive and results in a violation of at least someindividuals' rights. The result provides a rationale for the inherentdifficulty of reform in the presence of asymmetric information.
"There is nothing more difficult to carry out, nor more doubtful ofsuccess, nor more dangerous to handle, than to initiate a new order ofthings."
Niccolò Machiavelli, The Prince (1532)     

Finitely Many Players with Bounded Recall in Infinitely Repeated Games

We study the set of limit points of equilibrium payoffs in n-player repeated games, with bounded recall, when the memory capacities of all the players grow to infinity. Two main issues are explored: (i) whether differential information enables players to play correlatively, and (ii) the extent to which boundedly rational players can learn others′ behavior patterns and conceal their own. Journal of Economic Literature Classification Number: 026.     

A note on the evaluation of information in zero-sum repeated games

Two players play a zero-sum repeated game with incomplete information. Before the game starts one player receives a private signal that depends on the realized state of nature. The rules that govern the choice of the signal are determined by the information structure of the game. Different information structures induce different values. The value-of-information function of a game associates every information structure with the value it induces. We characterize those functions that are value-of-information functions for some zero-sum repeated game with incomplete information.     

Approachability with bounded memory

We study Blackwell's approachability in repeated games with vector payoffs when the approaching player is restricted to use strategies with bounded memory: either strategies with bounded recall, or strategies that can be implemented by finite automata. Our main finding is that the following three statements are equivalent for closed sets. (i) The set is approachable with bounded recall strategies. (ii) The set is approachable with strategies that can be implemented with finite automata. (iii) The set contains a convex approachable set. Using our results we show that (i) there are almost-regret-free strategies with bounded memory, (ii) there is a strategy with bounded memory to choose the best among several experts, and (iii) Hart and Mas-Colell's adaptive learning procedure can be achieved using strategies with bounded memory.     

Relative entropy in sequential decision problems

Consider an agent who faces a sequential decision problem. At each stage the agent takes an action and observes a stochastic outcome (e.g., daily prices, weather conditions, opponents' actions in a repeated game, etc.). The agent's stage-utility depends on his action, the observed outcome and on previous outcomes. We assume the agent is Bayesian and is endowed with a subjective belief over the distribution of outcomes. The agent's initial belief is typically inaccurate. Therefore, his subjectively optimal strategy is initially suboptimal. As time passes information about the true dynamics is accumulated and, depending on the compatibility of the belief with respect to the truth, the agent may eventually learn to optimize. We introduce the notion of relative entropy, which is a natural adaptation of the entropy of a stochastic process to the subjective set-up. We present conditions, expressed in terms of relative entropy, that determine whether the agent will eventually learn to optimize. It is shown that low entropy yields asymptotic optimal behavior. In addition, we present a notion of pointwise merging and link it with relative entropy.     

On the dynamic effects of using hired labor in the Kibbutz—theory and case studies

This study analyzes the effect of employing hired labor in the Kibbutz. The main motivations are the premises contained in the newly emerging “The Change” or “The New Kibbutz” approach. Using the traditional LMF model with heterogeneous labor, we show that, although using hired labor will improve the economic situation of the Kibbutz in the short-run, in the long-run Kibbutz membership will consist of only those types of labor to which the “Self Labor” principle applies.