10,421 research outputs found
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
Congestion, equilibrium and learning: The minority game
The minority game is a simple congestion game in which the players' main goal
is to choose among two options the one that is adopted by the smallest number
of players. We characterize the set of Nash equilibria and the limiting
behavior of several well-known learning processes in the minority game with an
arbitrary odd number of players. Interestingly, different learning processes
provide considerably different predictions
Joint strategy fictitious play with inertia for potential games
We consider multi-player repeated games involving a large number of players with large strategy spaces and enmeshed utility structures. In these ldquolarge-scalerdquo games, players are inherently faced with limitations in both their observational and computational capabilities. Accordingly, players in large-scale games need to make their decisions using algorithms that accommodate limitations in information gathering and processing. This disqualifies some of the well known decision making models such as ldquoFictitious Playrdquo (FP), in which each player must monitor the individual actions of every other player and must optimize over a high dimensional probability space. We will show that Joint Strategy Fictitious Play (JSFP), a close variant of FP, alleviates both the informational and computational burden of FP. Furthermore, we introduce JSFP with inertia, i.e., a probabilistic reluctance to change strategies, and establish the convergence to a pure Nash equilibrium in all generalized ordinal potential games in both cases of averaged or exponentially discounted historical data. We illustrate JSFP with inertia on the specific class of congestion games, a subset of generalized ordinal potential games. In particular, we illustrate the main results on a distributed traffic routing problem and derive tolling procedures that can lead to optimized total traffic congestion
CSMA Local Area Networking under Dynamic Altruism
In this paper, we consider medium access control of local area networks
(LANs) under limited-information conditions as befits a distributed system.
Rather than assuming "by rule" conformance to a protocol designed to regulate
packet-flow rates (e.g., CSMA windowing), we begin with a non-cooperative game
framework and build a dynamic altruism term into the net utility. The effects
of altruism are analyzed at Nash equilibrium for both the ALOHA and CSMA
frameworks in the quasistationary (fictitious play) regime. We consider either
power or throughput based costs of networking, and the cases of identical or
heterogeneous (independent) users/players. In a numerical study we consider
diverse players, and we see that the effects of altruism for similar players
can be beneficial in the presence of significant congestion, but excessive
altruism may lead to underuse of the channel when demand is low
On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games
In \emph{bandwidth allocation games} (BAGs), the strategy of a player
consists of various demands on different resources. The player's utility is at
most the sum of these demands, provided they are fully satisfied. Every
resource has a limited capacity and if it is exceeded by the total demand, it
has to be split between the players. Since these games generally do not have
pure Nash equilibria, we consider approximate pure Nash equilibria, in which no
player can improve her utility by more than some fixed factor through
unilateral strategy changes. There is a threshold (where
is a parameter that limits the demand of each player on a specific
resource) such that -approximate pure Nash equilibria always exist for
, but not for . We give both
upper and lower bounds on this threshold and show that the
corresponding decision problem is -hard. We also show that the
-approximate price of anarchy for BAGs is . For a restricted
version of the game, where demands of players only differ slightly from each
other (e.g. symmetric games), we show that approximate Nash equilibria can be
reached (and thus also be computed) in polynomial time using the best-response
dynamic. Finally, we show that a broader class of utility-maximization games
(which includes BAGs) converges quickly towards states whose social welfare is
close to the optimum
- …