In this note we consider the following high-order rational difference equation xn = 1+ k ∏ i=1 (1− xn−i ) k ∑ i=1 xn−i , n = 0, 1, . . . , where k ≥ 3 is odd number, x−k , x−k+1, x−k+2, . . . , x−1 is positive numbers. We obtain the boundedness of positive solutions for the above equation, and with the perturbation of initial values, we mainly use the transformation method to prove that the pos...

Mechanism design theory strongly relies on the concept of Nash equilibrium. However, studies of experimental games show that Nash equilibria are rarely played and that subjects may be thinking only a finite number of iterations. We study one of the most influential benchmarks of mechanism design theory, the expected externality mechanism (D’Aspremont, GerardVaret, 1979) in a finite-depth enviro...

Probabilism is committed to two theses: 1) Opinion comes in degrees—call them degrees of belief, or credences. 2) The degrees of belief of a rational agent obey the probability calculus. Correspondingly, a natural way to argue for probabilism is: i) to give an account of what degrees of belief are,

the purpose of this study is to present an approximate numerical method for solving high order linear fredholm-volterra integro-differential equations in terms of rational chebyshev functions under the mixed conditions. the method is based on the approximation by the truncated rational chebyshev series. finally, the effectiveness of the method is illustrated in several numerical examples. the p...

We study the behaviour of rational agents in exchange protocols which rely on trustees. We allow malicious parties to compromise the trustee by paying a cost and, thereby, present a game analysis that advocates exchange protocols which induce balanced risks on the participants. We also present a risk-balanced protocol for fair confidential secret comparison.

with y−s, y−s+1, . . . , y−1 ∈ (0,∞) and k, m ∈ {1, 2, 3, 4, . . .}, where s = k+m. We prove that if gcd(2k,m) = 1, then solutions to this equation are asymptotically 2k-periodic. This generalizes the corresponding result for m = 3 and k = 1, proved in K. S. Berenhaut et al., Periodic Solutions of the Rational Difference Equation yn = yn−3+yn−4 yn−1 ,Journal of Difference Equations and Applicat...

Surveys are frequently used by businesses and governments to elicit information about the public’s preferences. They have become the most common way to gather preference information regarding goods, that are not (or are not yet) bought or sold in markets. In this paper we apply the standard neoclassical economic framework to generate predictions about how rational agents would answer such surve...