The difficulty to write successful 19x19 go programs lies not only in the combinatorial complexity of go but also in the complexity of designing a good evaluation function containing a lot of knowledge. Leaving these obstacles aside, this paper defines very-little-knowledge evaluation functions used by programs playing on very small boards. The evaluation functions are based on two mathematical...

Aggregation functions and utility functions belong to very interesting parts of modern decision making theory. We develop basic concept of the connection of aggregation functions theory and utility theory to determine gross annual premium in general insurance. We introduce specific values of the gross annual premium on the basis of aggregation of the person’s utility functions which were determ...

Suppose the agent has preferences over consumption and labor represented by the utility function u (c, l) that we assume separable and quasi-linear such that u (c, l) = c v (l). We assume that v0 (l) > 0 and v00 (l) 0. Each agent earns income z = nl when supplying l hours of labor and consumes c = nl T (nl) after taxes. Individuals are heterogeneous in the salary n that represents their type an...

There exist several characterizations of concavity for univariate functions. One of them states that a function is concave if and only if it has nonincreasing differences. This definition provides a natural generalization of concavity for multivariate functions called inframodularity. Inframodular transfers are defined and it is shown that a finite lottery is preferred to another by all expecte...

We study multiple unit Discriminative auctions when the bidders share logconcave utility functions and investigate the effects of bidders risk preferences on their bid functions when all bidders share a common utility function and when the bidders exhibit different risk preferences. We extend the existing findings from single unit auctions to multiple unit Discriminative auctions,from concave u...

We present some simple utility functions whose Marshallian demand functions possess the Giffen property: at some price-wealth pairs, the demand for a good marginally increases in response to an increase in its own price. The utility functions satisfy standard preference properties throughout the usual consumption set of nonnegative bundles: continuity, monotonicity, and convexity.

We study fairness in a multicast network. We assume that the source hierarchically encodes its signal and the hierarchical structure is predetermined. We study fair allocation of utilities, where utility of a bandwidth can be the number of layers or the bandwidth itself, or any other function of the bandwidth depending on system requirements. The utility function is not strictly increasing in g...

We study fairness in a multicast network. We assume that the source hierarchically encodes its signal and the hierarchical structure is predetermined. We study fair allocation of utilities, where utility of a bandwidth can be the number of layers or the bandwidth itself, or any other function of the bandwidth depending on system requirements. The utility function is not strictly increasing in g...

We identify restrictions on a decision maker’s utility function that are both necessary and sufficient to preserve dominance reasoning in each of two versions of the Two-Envelope Paradox (TEP). For the classical TEP, the utility function must satisfy a certain recurrence inequality. For the St. Petersburg TEP, the utility function must be bounded above asymptotically by a power function, which ...