7,152 research outputs found
Feature-weighted categorized play across symmetric games
Experimental game theory studies the behavior of agents who face a stream of one-shot games as a form of learning. Most literature focuses on a single recurring identical game. This paper embeds single-game learning in a broader perspective, where learning can take place across similar games. We posit that agents categorize games into a few classes and tend to play the same action within a class. The agent’s categories are generated by combining game features (payoffs) and individual motives. An individual categorization is experience-based, and may change over time. We demonstrate our approach by testing a robust (parameter-free) model over a large body of independent experimental evidence over 2 × 2 symmetric games. The model provides a very good fit across games, performing remarkably better than standard learning models
The minority game: An economics perspective
This paper gives a critical account of the minority game literature. The
minority game is a simple congestion game: players need to choose between two
options, and those who have selected the option chosen by the minority win. The
learning model proposed in this literature seems to differ markedly from the
learning models commonly used in economics. We relate the learning model from
the minority game literature to standard game-theoretic learning models, and
show that in fact it shares many features with these models. However, the
predictions of the learning model differ considerably from the predictions of
most other learning models. We discuss the main predictions of the learning
model proposed in the minority game literature, and compare these to
experimental findings on congestion games.Comment: 30 pages, 4 figure
Unbeatable Imitation
We show that for many classes of symmetric two-player games, the simple
decision rule "imitate-the-best" can hardly be beaten by any other decision
rule. We provide necessary and sufficient conditions for imitation to be
unbeatable and show that it can only be beaten by much in games that are of the
rock-scissors-paper variety. Thus, in many interesting examples, like 2x2
games, Cournot duopoly, price competition, rent seeking, public goods games,
common pool resource games, minimum effort coordination games, arms race,
search, bargaining, etc., imitation cannot be beaten by much even by a very
clever opponent
Query Complexity of Approximate Equilibria in Anonymous Games
We study the computation of equilibria of anonymous games, via algorithms
that may proceed via a sequence of adaptive queries to the game's payoff
function, assumed to be unknown initially. The general topic we consider is
\emph{query complexity}, that is, how many queries are necessary or sufficient
to compute an exact or approximate Nash equilibrium.
We show that exact equilibria cannot be found via query-efficient algorithms.
We also give an example of a 2-strategy, 3-player anonymous game that does not
have any exact Nash equilibrium in rational numbers. However, more positive
query-complexity bounds are attainable if either further symmetries of the
utility functions are assumed or we focus on approximate equilibria. We
investigate four sub-classes of anonymous games previously considered by
\cite{bfh09, dp14}.
Our main result is a new randomized query-efficient algorithm that finds a
-approximate Nash equilibrium querying
payoffs and runs in time . This improves on the running
time of pre-existing algorithms for approximate equilibria of anonymous games,
and is the first one to obtain an inverse polynomial approximation in
poly-time. We also show how this can be utilized as an efficient
polynomial-time approximation scheme (PTAS). Furthermore, we prove that
payoffs must be queried in order to find any
-well-supported Nash equilibrium, even by randomized algorithms
Experience-weighted Attraction Learning in Normal Form Games
In ‘experience-weighted attraction’ (EWA) learning, strategies have attractions that reflect initial predispositions, are updated based on payoff experience, and determine choice probabilities according to some rule (e.g., logit). A key feature is a parameter δ that weights the strength of hypothetical reinforcement of strategies that were not chosen according to the payoff they would have yielded, relative to reinforcement of chosen strategies according to received payoffs. The other key features are two discount rates, φ and ρ, which separately discount previous attractions, and an experience weight. EWA includes reinforcement learning and weighted fictitious play (belief learning) as special cases, and hybridizes their key elements. When δ= 0 and ρ= 0, cumulative choice reinforcement results. When δ= 1 and ρ=φ, levels of reinforcement of strategies are exactly the same as expected payoffs given weighted fictitious play beliefs. Using three sets of experimental data, parameter estimates of the model were calibrated on part of the data and used to predict a holdout sample. Estimates of δ are generally around .50, φ around .8 − 1, and ρ varies from 0 to φ. Reinforcement and belief-learning special cases are generally rejected in favor of EWA, though belief models do better in some constant-sum games. EWA is able to combine the best features of previous approaches, allowing attractions to begin and grow flexibly as choice reinforcement does, but reinforcing unchosen strategies substantially as belief-based models implicitly do
Dynamical selection of Nash equilibria using Experience Weighted Attraction Learning: emergence of heterogeneous mixed equilibria
We study the distribution of strategies in a large game that models how
agents choose among different double auction markets. We classify the possible
mean field Nash equilibria, which include potentially segregated states where
an agent population can split into subpopulations adopting different
strategies. As the game is aggregative, the actual equilibrium strategy
distributions remain undetermined, however. We therefore compare with the
results of Experience-Weighted Attraction (EWA) learning, which at long times
leads to Nash equilibria in the appropriate limits of large intensity of
choice, low noise (long agent memory) and perfect imputation of missing scores
(fictitious play). The learning dynamics breaks the indeterminacy of the Nash
equilibria. Non-trivially, depending on how the relevant limits are taken, more
than one type of equilibrium can be selected. These include the standard
homogeneous mixed and heterogeneous pure states, but also \emph{heterogeneous
mixed} states where different agents play different strategies that are not all
pure. The analysis of the EWA learning involves Fokker-Planck modeling combined
with large deviation methods. The theoretical results are confirmed by
multi-agent simulations.Comment: 35 pages, 16 figure
Contagion through learning
We study learning in a large class of complete information normal form games. Players continually face new strategic situations and must form beliefs by extrapolation from similar past situations. We characterize the long-run outcomes of learning in terms of iterated dominance in a related incomplete information game with subjective priors. The use of extrapolations in learning may generate contagion of actions across games even if players learn only from games with payoffs very close to the current ones. Contagion may lead to unique long-run outcomes where multiplicity would occur if players learned through repeatedly playing the same game. The process of contagion through learning is formally related to contagion in global games, although the outcomes generally differ.Similarity, learning, contagion, case-based reasoning, global games
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