We discuss infinite zero-sum perfect-information games with more than two players. They are not determined in the traditional sense, but as soon as you fix a preference function for the players and assume common knowledge of rationality and this preference function among the players, you get determinacy for open and closed payoff sets. 2000 AMS Mathematics Subject Classification. 91A06 91A10 03...

In this paper, we are interested in a preference function that associates to a profile of linear orders the set of its corresponding prudent orders. We will introduce axioms that will restrict the set of linear orders to the set of prudent orders. By slightly adapting these axioms, the prudent order preference function can be fully characterized.

Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space.

We address the problem of aggregating demand across a group of consumers, who are identical in terms of wealth and face identical price vectors, but vary in their chosen consumption bundles. We show that, when a stochastic demand function is constructed to aggregate a number of deterministic demand functions, satisfaction of the weak axiom of stochastic revealed preference by this stochastic de...

The problem of nding the solution set of alternatives when a linguistic preference relation represents a collective preference is analyzed. Three choice sets for a linguistic preference relation are studied and some relations between them are pointed out. The concept of linguistic choice function is introduced and some particular cases are analyzed.

Abstract. We study the optimal rates of convergence for estimating a prior distribution over a VC class from a sequence of independent data sets respectively labeled by independent target functions sampled from the prior. We specifically derive upper and lower bounds on the optimal rates under a smoothness condition on the correct prior, with the number of samples per data set equal the VC dime...

Multi-Attribute Reverse Auctions (MARAs) are excellent protocols to automate negotiation among sellers. Eliciting the buyer′s preferences and determining the winner are both challenging problems for MARAs. To solve these problems, we propose two algorithms namely MAUT* and CP-net*, which are respectively the improvement of the Multi-Attribute Utility Theory (MAUT) and constrained CP-net. The bu...

In this paper, we describe a methodology for capturing player experience while interacting with a game and we present a data-driven approach for modeling this interaction. We believe the best way to adapt games to a specific player is to use quantitative models of player experience derived from the in-game interaction. Therefore, we rely on crowd-sourced data collected about game context, playe...

We consider the challenge of preference elicitation in systems that help users discover the most desirable item(s) within a given database. Past work on preference elicitation focused on structured models that provide a factored representation of users’ preferences. Such models require less information to construct and support efficient reasoning algorithms. This paper makes two substantial con...