Consider a set of n players. We suppose that each game involves two players, that there is some unknown player who wins each game it plays with a probability greater than 1/2, and that our objective is to determine this best player. Under the requirement that the policy employed guarantees a correct choice with a probability of at least some specified value, we look for a policy that has a relatively small expected number of games played before decision. We consider this problem both under the assumption that the best player wins each game with a probability of at least some specified value >1/2, and under a Bayesian assumption that the probability that player i wins a game against player j is its value divided by the sum of the values, where the values are the unknown values of n independent and identically distributed exponential random variables. In the former case, we propose a policy where chosen pairs play a match that ends when one of them has had a specified number of wins more than the other; in the latter case, we propose a Thompson sampling type rule.
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Tit-for-tat dynamics and market volatility
We consider tit-for-tat dynamics in production markets, where there is a set of
- NSF-PAR ID:
- 10488252
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Nonlinearity
- Volume:
- 37
- Issue:
- 3
- ISSN:
- 0951-7715
- Format(s):
- Medium: X Size: Article No. 035006
- Size(s):
- Article No. 035006
- Sponsoring Org:
- National Science Foundation
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