97,331 research outputs found
On the transition to efficiency in Minority Games
The existence of a phase transition with diverging susceptibility in batch
Minority Games (MGs) is the mark of informationally efficient regimes and is
linked to the specifics of the agents' learning rules. Here we study how the
standard scenario is affected in a mixed population game in which agents with
the `optimal' learning rule (i.e. the one leading to efficiency) coexist with
ones whose adaptive dynamics is sub-optimal. Our generic finding is that any
non-vanishing intensive fraction of optimal agents guarantees the existence of
an efficient phase. Specifically, we calculate the dependence of the critical
point on the fraction of `optimal' agents focusing our analysis on three
cases: MGs with market impact correction, grand-canonical MGs and MGs with
heterogeneous comfort levels.Comment: 12 pages, 3 figures; contribution to the special issue "Viewing the
World through Spin Glasses" in honour of David Sherrington on the occasion of
his 65th birthda
Strategy correlations and timing of adaptation in Minority Games
We study the role of strategy correlations and timing of adaptation for the
dynamics of Minority Games, both simulationally and analytically. Using the
exact generating functional approach a la De Dominicis we compute the phase
diagram and the behaviour of batch and on-line games with correlated
strategies, complementing exisiting replica studies of their statics. It is
shown that the timing of adaptation can be relevant; while conventional games
with uncorrelated strategies are nearly insensitive to the choice of on-line
versus batch learning, we find qualitative differences when anti-correlations
are present in the strategy assignments. The available standard approximations
for the volatility in terms of persistent order parameters in the stationary
ergodic states become unreliable in batch games under such circumstances. We
then comment on the role of oscillations and the relation to the breakdown of
ergodicity. Finally, it is discussed how the generating functional formalism
can be used to study mixed populations of so-called `producers' and
`speculators' in the context of the batch minority games.Comment: 15 pages, 13 figures, EPJ styl
Entropic selection of Nash equilibrium
This study argues that Nash equilibria with less variations in players' best responses are more appealing. To that regard, a notion measuring such variations, the entropic selection of Nash equilibrium, is presented: For any given Nash equilibrium, we consider the cardinality of the support of a player's best response against others' strategies that are sufficiently close to the
behavior specified. These cardinalities across players are then aggregated with a real-valued function on whose form we impose no restrictions apart from the natural limitation to nondecreasingness in order to obtain equilibria with less variations. We prove that the entropic selection of Nash equilibrium is non-empty and admit desirable properties. Some well-known games, each of which display important insights about virtues / problems of various equilibrium
notions, are considered; and, in all of these games our notion displays none of the criticisms associated with these examples. These examples also show that our notion does not have any containment relations with other associated and well-known refinements, perfection, properness and persistence
Do male managers increase risk-taking of female teams? Evidence from the NCAA
We analyze the effect of the coach's gender on risk-taking in women sports teams using data taken from National Collegiate Athletic Association (NCAA) basketball games. We find that the coach's gender has a sizable and significant effect on risk-taking, a finding that is robust to several empirical strategies, including an instrumental variable approach. In particular, we find that risk-taking among teams with a male head coach is 5 percentage points greater than that in teams with a female head coach. This gap is persistent over time and across intermediate game standings. The fact that risk-taking has a significantly positive effect on game success suggests that female coaches should be more risk-taking.Series: Department of Economics Working Paper Serie
Rationalizability and Minimal Complexity in Dynamic Games
This paper presents a formal epistemic framework for dynamic games in which players, during the course of the game, may revise their beliefs about the opponents'' utility functions. We impose three key conditions upon the players'' beliefs: (a) throughout the game, every move by the opponent should be interpreted as being part of a rational strategy, (b) the belief about the opponents'' relative ranking of two strategies should not be revised unless one is certain that the opponent has decided not to choose one of these strategies, and (c) the players'' initial beliefs about the opponents'' utility functions should agree on a given profile u of utility functions. Types that, throughout the game, respect common belief about these three events, are called persistently rationalizable for the profile u of utility functions. It is shown that persistent rationalizability implies the backward induction procedure in generic games with perfect information. We next focus on persistently rationalizable types for u that hold a theory about the opponents of ``minimal complexity'''', resulting in the concept of minimal rationalizability. For two-player simultaneous move games, minimal rationalizability is equivalent to the concept of Nash equilibrium strategy. In every outside option game, as defined by van Damme (1989), minimal rationalizability uniquely selects the forward induction outcome.microeconomics ;
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