2,550 research outputs found
Mixing times and moving targets
We consider irreducible Markov chains on a finite state space. We show that
the mixing time of any such chain is equivalent to the maximum, over initial
states and moving large sets , of the hitting time of
starting from . We prove that in the case of the -dimensional torus the
maximum hitting time of moving targets is equal to the maximum hitting time of
stationary targets. Nevertheless, we construct a transitive graph where these
two quantities are not equal, resolving an open question of Aldous and Fill on
a "cat and mouse" game
Cops vs. Gambler
We consider a variation of cop vs.\ robber on graph in which the robber is
not restricted by the graph edges; instead, he picks a time-independent
probability distribution on and moves according to this fixed
distribution. The cop moves from vertex to adjacent vertex with the goal of
minimizing expected capture time. Players move simultaneously. We show that
when the gambler's distribution is known, the expected capture time (with best
play) on any connected -vertex graph is exactly . We also give bounds on
the (generally greater) expected capture time when the gambler's distribution
is unknown to the cop.Comment: 6 pages, 0 figure
Contract Incentives and Effort
In a prevailing employment contract, the agent receives a proportional split of commissions. Alternatively, the agent receives a contract paying 100% of revenue above a fixed payment to the firm. In this contract the firm has a prior payment position, similar to a landlord or lender. The coexistence of these equity-only and debt-equity type contracts allows testing incentives for productivity and effort for U.S. real estate licensees. Hourly wages and productivity are increasing in the agent's split, up to and including 100%. Effort as measured by hours worked also positively affected by the split. The contract incentives motivate productivity and induce effort without requiring monitoring.
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