1,284 research outputs found
Robustness to Strategic Uncertainty (Revision of DP 2010-70)
We model a playerâs uncertainty about other playersâ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every playerâs strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.Nash equilibrium;refinement;strategic uncertainty;price competition;Bertrand competition;bargaining;Nash demand game
Emergence of Cooperation and Organization in an Evolutionary Game
A binary game is introduced and analysed. N players have to choose one of the
two sides independently and those on the minority side win. Players uses a
finite set of ad hoc strategies to make their decision, based on the past
record. The analysing power is limited and can adapt when necessary.
Interesting cooperation and competition pattern of the society seem to arise
and to be responsive to the payoff function.Comment: 8 pages, 13 figure
Modeling the Evolution of Differences in Variability Between Sexes
An elementary mathematical theory based on a âselectivity-variabilityâ principle is proposed to address a question raised by Charles Darwin, namely, how one sex of a sexually dimorphic species might tend to evolve with greater variability than the other sex. Two mathematical models of the principle are presented: a discrete-time one-step probabilistic model of the short-term behavior of the subpopulations of a given sex, with an example using normally distributed perceived fitness values; and a continuous-time deterministic coupled ODE model for the long-term asymptotic behavior of the expected sizes of the subpopulations, with an example using exponentially distributed fitness levels
Robustness to Strategic Uncertainty (Revision of DP 2010-70)
We model a playerâs uncertainty about other playersâ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every playerâs strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.
Social Dilemmas and Cooperation in Complex Networks
In this paper we extend the investigation of cooperation in some classical
evolutionary games on populations were the network of interactions among
individuals is of the scale-free type. We show that the update rule, the payoff
computation and, to some extent the timing of the operations, have a marked
influence on the transient dynamics and on the amount of cooperation that can
be established at equilibrium. We also study the dynamical behavior of the
populations and their evolutionary stability.Comment: 12 pages, 7 figures. to appea
Evolution of Coordination in Social Networks: A Numerical Study
Coordination games are important to explain efficient and desirable social
behavior. Here we study these games by extensive numerical simulation on
networked social structures using an evolutionary approach. We show that local
network effects may promote selection of efficient equilibria in both pure and
general coordination games and may explain social polarization. These results
are put into perspective with respect to known theoretical results. The main
insight we obtain is that clustering, and especially community structure in
social networks has a positive role in promoting socially efficient outcomes.Comment: preprint submitted to IJMP
Experimental analysis of lateral impact on planar brittle material
The fragmentation of alumina and glass plates due to lateral impact is
studied. A few hundred plates have been fragmented at different impact
velocities and the produced fragments are analyzed. The method employed in this
work allows one to investigate some geometrical properties of the fragments,
besides the traditional size distribution usually studied in former
experiments. We found that, although both materials exhibit qualitative similar
fragment size distribution function, their geometrical properties appear to be
quite different. A schematic model for two-dimensional fragmentation is also
presented and its predictions are compared to our experimental results. The
comparison suggests that the analysis of the fragments' geometrical properties
constitutes a more stringent test of the theoretical models' assumptions than
the size distribution
Selection of noise level in strategy adoption for spatial social dilemmas
We studied spatial Prisoner's Dilemma and Stag Hunt games where both the
strategy distribution and the players' individual noise level could evolve to
reach higher individual payoff. Players are located on the sites of different
two-dimensional lattices and gain their payoff from games with their neighbors
by choosing unconditional cooperation or defection. The way of strategy
adoption can be characterized by a single (temperature-like) parameter
describing how strongly adoptions depend on the payoff-difference. If we start
the system from a random strategy distribution with many different player
specific parameters, the simultaneous evolution of strategies and
parameters drives the system to a final stationary state where only one
value remains. In the coexistence phase of cooperator and defector strategies
the surviving parameter is in good agreement with the noise level that
ensures the highest cooperation level if uniform is supposed for all
players. In this paper we give a thorough overview about the properties of this
evolutionary process.Comment: 10 two-column pages, 10 figures; accepted for publication in Physical
Review
Random replicators with asymmetric couplings
Systems of interacting random replicators are studied using generating
functional techniques. While replica analyses of such models are limited to
systems with symmetric couplings, dynamical approaches as presented here allow
specifically to address cases with asymmetric interactions where there is no
Lyapunov function governing the dynamics. We here focus on replicator models
with Gaussian couplings of general symmetry between p>=2 species, and discuss
how an effective description of the dynamics can be derived in terms of a
single-species process. Upon making a fixed point ansatz persistent order
parameters in the ergodic stationary states can be extracted from this process,
and different types of phase transitions can be identified and related to each
other. We discuss the effects of asymmetry in the couplings on the order
parameters and the phase behaviour for p=2 and p=3. Numerical simulations
verify our theory. For the case of cubic interactions numerical experiments
indicate regimes in which only a finite number of species survives, even when
the thermodynamic limit is considered.Comment: revised version, removed some mathematical parts, discussion of
negatively correlated couplings added, figures adde
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