This sequel to previous chapters on objective and subjective expected utility reviews conditions for players in a non-cooperative game to be Bayesian rational — i.e., to choose a strategy maximizing the expectation of each von Neumann–Morgenstern utility function in a unique cardinal equivalence class. In classical Nash equilibrium theory, players’ mixed strategies involve objective probabiliti...

We present a tutorial on Bayesian optimization, a method of finding the maximum of expensive cost functions. Bayesian optimization employs the Bayesian technique of setting a prior over the objective function and combining it with evidence to get a posterior function. This permits a utility-based selection of the next observation to make on the objective function, which must take into account b...

In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or more argument. We make the case that shape constraints are often appropriate in at least two important application areas of Bayesian optimization: (1) hyperpar...

Decision-theoretic rough set (DTRS) model, proposed by Yao in the early 1990’s, introduces Bayesian decision procedure and loss function in rough set theory. Considering utility function in decision processing, utility-based decision-theoretic rough set model (UDTRS) is given in this paper. The utility of the positive region, the boundary region and the negative region are obtained respectively...

In a competitive market, customer decision is made to maximize his utility. It can be assumed that risk of losing a supply chain’s customer can be defined based on products utility from customer point of view. This paper takes account of product price and service level as competition criteria. The proposed model is based on non-cooperative game theory, for one-manufacturer and one-retailer supp...

We design efficient algorithms to compute truthful mechanisms for risk-averse sellers, in Bayesian single-parameter and multi-parameter settings. We model risk aversion by a concave utility function, where the the seller maximizes its expected utility. Much earlier work on Bayesian mechanism design has focused on maximizing expected revenue, and no succinct characterization of expected utility ...

Background and Objectives: The selection of the sustainable supplier is important for any industry. Medical centers are not an exception in this case, and selecting the best sustainable supplier is a major step towards increasing their productivity. This paper, using the Data Envelopment Analysis and then using Multi-Attributed Utility Theory as a backup approach to fix errors, attempts t...

This paper discusses our newly developed object-oriented computer program IDASS which intends to support interactive decision analysis under uncertainty in the IDSS environments. IDASS intends to support DM’s subjective decisions based on expected utility theory and Bayesian statistics. The interactive processes of logical thinking of DM are aided on the axiomatic basis through the consistency ...