38,032 research outputs found
Strategic Resource Dependence
We consider a situation where an exhaustible-resource seller faces demand from a buyer who has a perfect substitute but there is a time-to-build delay for the substitute. We that find in this simple framework the basic implications of the Hotelling model (1931) are reversed: over time the stock declines but supplies increase up to the point where the buyer decides to switch. Under such a threat of demand change, the supply does not reflect the true current resource scarcity but leads to increased future scarcity, felt during the transition to the substitute supplies. The analysis suggests a perspective on costs of oil dependence.Dynamic Bilateral Monopoly, Markov-Perfect Equilibrium, Depletable Resources, Energy, Alternative Fuels, Oil Dependence
Separable and Low-Rank Continuous Games
In this paper, we study nonzero-sum separable games, which are continuous
games whose payoffs take a sum-of-products form. Included in this subclass are
all finite games and polynomial games. We investigate the structure of
equilibria in separable games. We show that these games admit finitely
supported Nash equilibria. Motivated by the bounds on the supports of mixed
equilibria in two-player finite games in terms of the ranks of the payoff
matrices, we define the notion of the rank of an n-player continuous game and
use this to provide bounds on the cardinality of the support of equilibrium
strategies. We present a general characterization theorem that states that a
continuous game has finite rank if and only if it is separable. Using our rank
results, we present an efficient algorithm for computing approximate equilibria
of two-player separable games with fixed strategy spaces in time polynomial in
the rank of the game
A Simple Logic of Functional Dependence
This paper presents a simple decidable logic of functional dependence LFD,
based on an extension of classical propositional logic with dependence atoms
plus dependence quantifiers treated as modalities, within the setting of
generalized assignment semantics for first order logic. The expressive
strength, complete proof calculus and meta-properties of LFD are explored.
Various language extensions are presented as well, up to undecidable
modal-style logics for independence and dynamic logics of changing dependence
models. Finally, more concrete settings for dependence are discussed:
continuous dependence in topological models, linear dependence in vector
spaces, and temporal dependence in dynamical systems and games.Comment: 56 pages. Journal of Philosophical Logic (2021
Local Identification in Empirical Games of Incomplete Information
This paper studies identification for a broad class of empirical games in a general functional setting. Global identification results are known for some specific models, for instance in some standard auction models. We use functional formulations to obtain general criteria for local identification. These criteria can be applied to both parametric and nonparametric models, as well as models with asymmetry among players and affiliated private information. A benchmark model is developed where the structural parameters of interest are the distribution of private information and an additional dissociated parameter, such as a parameter of risk aversion. Criteria are derived for some standard auction models, games with exogenous variables, games with randomized strategies, such as mixed strategies, and games with strategic functions that cannot be derived analytically
Evolutionary games and quasispecies
We discuss a population of sequences subject to mutations and
frequency-dependent selection, where the fitness of a sequence depends on the
composition of the entire population. This type of dynamics is crucial to
understand the evolution of genomic regulation. Mathematically, it takes the
form of a reaction-diffusion problem that is nonlinear in the population state.
In our model system, the fitness is determined by a simple mathematical game,
the hawk-dove game. The stationary population distribution is found to be a
quasispecies with properties different from those which hold in fixed fitness
landscapes.Comment: 7 pages, 2 figures. Typos corrected, references updated. An exact
solution for the hawks-dove game is provide
Competition in Wireless Systems via Bayesian Interference Games
We study competition between wireless devices with incomplete information
about their opponents. We model such interactions as Bayesian interference
games. Each wireless device selects a power profile over the entire available
bandwidth to maximize its data rate. Such competitive models represent
situations in which several wireless devices share spectrum without any central
authority or coordinated protocol.
In contrast to games where devices have complete information about their
opponents, we consider scenarios where the devices are unaware of the
interference they cause to other devices. Such games, which are modeled as
Bayesian games, can exhibit significantly different equilibria. We first
consider a simple scenario of simultaneous move games, where we show that the
unique Bayes-Nash equilibrium is where both devices spread their power equally
across the entire bandwidth. We then extend this model to a two-tiered spectrum
sharing case where users act sequentially. Here one of the devices, called the
primary user, is the owner of the spectrum and it selects its power profile
first. The second device (called the secondary user) then responds by choosing
a power profile to maximize its Shannon capacity. In such sequential move
games, we show that there exist equilibria in which the primary user obtains a
higher data rate by using only a part of the bandwidth.
In a repeated Bayesian interference game, we show the existence of reputation
effects: an informed primary user can bluff to prevent spectrum usage by a
secondary user who suffers from lack of information about the channel gains.
The resulting equilibrium can be highly inefficient, suggesting that
competitive spectrum sharing is highly suboptimal.Comment: 30 pages, 3 figure
Strategic Freedom, Constraint, and Symmetry in One-period Markets with Cash and Credit Payment
In order to explain in a systematic way why certain combinations of market, financial, and legal structures may be intrinsic to certain capabilities to exchange real goods, we introduce criteria for abstracting the qualitative functions of markets. The criteria involve the number of strategic freedoms the combined institutions, considered as formalized strategic games, present to traders, the constraints they impose, and the symmetry with which those constraints are applied to the traders. We pay particular attention to what is required to make these "strategic market games" well-defined, and to make various solutions computable by the agents within the bounds on information and control they are assumed to have. As an application of these criteria, we present a complete taxonomy of the minimal one-period exchange economies with symmetric information and inside money. A natural hierarchy of market forms is observed to emerge, in which institutionally simpler markets are often found to be more suitable to fewer and less-diversified traders, while the institutionally richer markets only become functional as the size and diversity of their users gets large.Strategic market games, Clearinghouses, Credit evaluation, Default
Properly Quantized History Dependent Parrondo Games, Markov Processes, and Multiplexing Circuits
In the context of quantum information theory, "quantization" of various
mathematical and computational constructions is said to occur upon the
replacement, at various points in the construction, of the classical
randomization notion of probability distribution with higher order
randomization notions from quantum mechanics such as quantum superposition with
measurement. For this to be done "properly", a faithful copy of the original
construction is required to exist within the new "quantum" one, just as is
required when a function is extended to a larger domain. Here procedures for
extending history dependent Parrondo games, Markov processes and multiplexing
circuits to their "quantum" versions are analyzed from a game theoretic
viewpoint, and from this viewpoint, proper quantizations developed
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