49,757 research outputs found
Zero-sum games with charges
We consider two-player zero-sum games with infinite action spaces and bounded payoff functions. The players' strategies are finitely additive probability measures, called charges. Since a strategy profile does not always induce a unique expected payoff, we distinguish two extreme attitudes of players. A player is viewed as pessimistic if he always evaluates the range of possible expected payoffs by the worst one, and a player is viewed as optimistic if he always evaluates it by the best one. This approach results in a definition of a pessimistic and an optimistic guarantee level for each player. We provide an extensive analysis of the relation between these guarantee levels, and connect them to the classical guarantee levels, and to other known techniques to define expected payoffs, based on computation of double integrals. In addition, we also examine existence of optimal strategies with respect to these guarantee levels
A game theoretic analysis of the Waterloo campaign and some comments on the analytic narrative project
The paper has a twofold aim. On the one hand, it provides what appears to be the first game-theoretic modeling of Napoleonâs last campaign, which ended dramatically on 18 June 1815 at Waterloo. It is specifically concerned with the decision Napoleon made on 17 June 1815 to detach part of his army against the Prussians he had defeated, though not destroyed, on 16 June at Ligny. Military historians agree that this decision was crucial but disagree about whether it was rational. Hypothesizing a zero-sum game between Napoleon and BlĂŒcher, and computing its solution, we show that it could have been a cautious strategy on the former's part to divide his army, a conclusion which runs counter to the charges of misjudgement commonly heard since Clausewitz. On the other hand, the paper addresses methodological issues. We defend its case study against the objections of irrelevance that have been raised elsewhere against âanalytic narrativesâ, and conclude that military campaigns provide an opportunity for successful application of the formal theories of rational choice. Generalizing the argument, we finally investigate the conflict between narrative accounts â the historians' standard mode of expression â and mathematical modeling.NapolĂ©on; BlĂŒcher; Grouchy; Waterloo; military history; rational choice theories; game theory; zero-sum two-person games; analytical narrative
Advance reservation games
Advance reservation (AR) services form a pillar of several branches of the economy, including transportation,
lodging, dining, and, more recently, cloud computing. In this work, we use game theory to analyze a slotted
AR system in which customers differ in their lead times. For each given time slot, the number of customers
requesting service is a random variable following a general probability distribution. Based on statistical
information, the customers decide whether or not to make an advance reservation of server resources in
future slots for a fee. We prove that only two types of equilibria are possible: either none of the customers
makes AR or only customers with lead time greater than some threshold make AR. Our analysis further
shows that the fee that maximizes the providerâs profit may lead to other equilibria, one of which yields zero
profit. In order to prevent ending up with no profit, the provider can elect to advertise a lower fee yielding
a guaranteed but smaller profit. We refer to the ratio of the maximum possible profit to the maximum
guaranteed profit as the price of conservatism. When the number of customers is a Poisson random variable, we prove that the price of conservatism is one in the single-server case, but can be arbitrarily high in a many-server system.CNS-1117160 - National Science Foundationhttp://people.bu.edu/staro/ACM_ToMPECS_AR.pdfAccepted manuscrip
Pricing in networks
This paper studies optimal pricing in networks in the presence of local consumption or price externalities. It analyzes the relation between prices and nodal centrality measures. Using an asymptotic approach, it shows that the ranking of optimal prices and strategies can be reduced to the lexicographic ranking of a specific vector of nodal characteristics. In particular, this result shows that with positive consumption externalities, prices are higher at nodes with higher degree, and with relative price externalities, prices are higher at nodes which have more neighbors of smaller degree.Social Networks, Network Externalities, Oligopolies
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A Tracing Method for Pricing Inter-Area Electricity Trades
In the context of liberalisation of electricity markets world wide, the need for agreed protocols for electricity trades between systems with different charges poses a special challenge. System operators need to know how much a given trade uses the network, in order to allocate an appropriate portion of their costs to that trade. This paper discusses a technique, tracing, for determining how much each of a number of trades uses different parts of the electricity network. The scheme is based on the assumption that at any network node, inflows are shared proportionally between outflows (and vice versa). The paper outlines the technique and shows how it could be applied to the problem of charging cross-border trades. The paper goes on to demonstrate that the technique has a game theoretic rationale, in that it produces the Shapley value solution to a game equivalent to this allocation problem
On the Efficiency of the Walrasian Mechanism
Central results in economics guarantee the existence of efficient equilibria
for various classes of markets. An underlying assumption in early work is that
agents are price-takers, i.e., agents honestly report their true demand in
response to prices. A line of research in economics, initiated by Hurwicz
(1972), is devoted to understanding how such markets perform when agents are
strategic about their demands. This is captured by the \emph{Walrasian
Mechanism} that proceeds by collecting reported demands, finding clearing
prices in the \emph{reported} market via an ascending price t\^{a}tonnement
procedure, and returns the resulting allocation. Similar mechanisms are used,
for example, in the daily opening of the New York Stock Exchange and the call
market for copper and gold in London.
In practice, it is commonly observed that agents in such markets reduce their
demand leading to behaviors resembling bargaining and to inefficient outcomes.
We ask how inefficient the equilibria can be. Our main result is that the
welfare of every pure Nash equilibrium of the Walrasian mechanism is at least
one quarter of the optimal welfare, when players have gross substitute
valuations and do not overbid. Previous analysis of the Walrasian mechanism
have resorted to large market assumptions to show convergence to efficiency in
the limit. Our result shows that approximate efficiency is guaranteed
regardless of the size of the market
Existence of equilibria in countable games: an algebraic approach
Although mixed extensions of finite games always admit equilibria, this is
not the case for countable games, the best-known example being Wald's
pick-the-larger-integer game. Several authors have provided conditions for the
existence of equilibria in infinite games. These conditions are typically of
topological nature and are rarely applicable to countable games. Here we
establish an existence result for the equilibrium of countable games when the
strategy sets are a countable group and the payoffs are functions of the group
operation. In order to obtain the existence of equilibria, finitely additive
mixed strategies have to be allowed. This creates a problem of selection of a
product measure of mixed strategies. We propose a family of such selections and
prove existence of an equilibrium that does not depend on the selection. As a
byproduct we show that if finitely additive mixed strategies are allowed, then
Wald's game admits an equilibrium. We also prove existence of equilibria for
nontrivial extensions of matching-pennies and rock-scissors-paper. Finally we
extend the main results to uncountable games
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