This paper continues the work initiated in [19]. We adopt the same model as in [19]. We show that the non-backward-induction equilibrium component may be evolutionarily stable for any population size in a finite stopping game where the two equilibrium components are terminated by different...

We consider a basic dynamic evolutionary model with rare mutation and a best-reply (or better-reply) selection mechanism. A state is evolutionarily stable if its long-term relative frequency of occurrence is bounded away from zero as the mutation rate decreases to zero. We prove that, for all...

Are good people motivated to behave in accordance the moral truth whatever it is? Michael Smith, who has named this motivation the de-dicto moral motivation, famously criticized it. According to Smith, good people are instead motivated directly by more concrete moral concerns, such as “the...

For a random permutation π on {1,2,…,n} for fixed n, and for M⊆{1,2,…,n}, we analyse the distribution of the combined length L=L(π,M) of all cycles of π that contain at least one element of M. We give a simple, explicit formula for the probability of every possible value for L (backed...

We add two results to the theory of consistent voting. Let M be the set of all survivors of some feasible elimination procedure. We prove that i) M can be computed in polynomial time for each profile of preferences and ii) M is characterized by anonymity, non- imposition, Maskin monotonicity,...

The logic of backward induction (BI) in perfect information (PI) games has been intensely scrutinized for the past quarter century. A major development came in 2002, when P. Battigalli and M. Sinischalchi (BS) showed that an outcome of a PI game is consistent with common strong belief of utility...

While the very first consensus protocols for the synchronous model were designed to match the <I>worst-case</I> lower bound, deciding in exactly t+1 rounds in all runs, it was soon realized that they could be strictly improved upon by <I>early stopping</I> protocols. These dominate the first ones, by always...</i></i>

We introduce asymptotic analysis of stochastic games with short-stage duration. The play of stage $k$, $k\geq 0$, of a stochastic game $\Gamma_\delta$ with stage duration $\delta$ is interpreted as the play in time $k\delta\leq t<(k+1)\delta$, and therefore the average payoff of the $n$-stage play per unit of time is the sum of the payoffs in the first $n$ stages divided by $n\delta$, and the $\lambda$-discounted present value of a payoff $g$ in stage $k$ is $\lambda^{k\delta} g$. We define convergence, strong convergence, and exact convergence of the data of a family $(\Gamma_\delta)_{\delta>0}$ as the stage duration $\delta$ goes to $0$, and study the...</(k+1)\delta$,>

Gale and Sotomayor (1985) have shown that in the Gale-Shapley matching algorithm (1962), the proposed-to side W (referred to as <i>women</i> there) can strategically force the W-optimal stable matching as the M-optimal one by truncating their preference lists, each woman possibly blacklisting <i>all but...</i>