2,377 research outputs found
Non-additive Security Games
We have investigated the security game under non-additive utility functions
Attainability in Repeated Games with Vector Payoffs
We introduce the concept of attainable sets of payoffs in two-player repeated
games with vector payoffs. A set of payoff vectors is called {\em attainable}
if player 1 can ensure that there is a finite horizon such that after time
the distance between the set and the cumulative payoff is arbitrarily
small, regardless of what strategy player 2 is using. This paper focuses on the
case where the attainable set consists of one payoff vector. In this case the
vector is called an attainable vector. We study properties of the set of
attainable vectors, and characterize when a specific vector is attainable and
when every vector is attainable.Comment: 28 pages, 2 figures, conference version at NetGCoop 201
Algorithmic Bayesian Persuasion
Persuasion, defined as the act of exploiting an informational advantage in
order to effect the decisions of others, is ubiquitous. Indeed, persuasive
communication has been estimated to account for almost a third of all economic
activity in the US. This paper examines persuasion through a computational
lens, focusing on what is perhaps the most basic and fundamental model in this
space: the celebrated Bayesian persuasion model of Kamenica and Gentzkow. Here
there are two players, a sender and a receiver. The receiver must take one of a
number of actions with a-priori unknown payoff, and the sender has access to
additional information regarding the payoffs. The sender can commit to
revealing a noisy signal regarding the realization of the payoffs of various
actions, and would like to do so as to maximize her own payoff assuming a
perfectly rational receiver.
We examine the sender's optimization task in three of the most natural input
models for this problem, and essentially pin down its computational complexity
in each. When the payoff distributions of the different actions are i.i.d. and
given explicitly, we exhibit a polynomial-time (exact) algorithm, and a
"simple" -approximation algorithm. Our optimal scheme for the i.i.d.
setting involves an analogy to auction theory, and makes use of Border's
characterization of the space of reduced-forms for single-item auctions. When
action payoffs are independent but non-identical with marginal distributions
given explicitly, we show that it is #P-hard to compute the optimal expected
sender utility. Finally, we consider a general (possibly correlated) joint
distribution of action payoffs presented by a black box sampling oracle, and
exhibit a fully polynomial-time approximation scheme (FPTAS) with a bi-criteria
guarantee. We show that this result is the best possible in the black-box model
for information-theoretic reasons
Dynamic Power Allocation Games in Parallel Multiple Access Channels
We analyze the distributed power allocation problem in parallel multiple
access channels (MAC) by studying an associated non-cooperative game which
admits an exact potential. Even though games of this type have been the subject
of considerable study in the literature, we find that the sufficient conditions
which ensure uniqueness of Nash equilibrium points typically do not hold in
this context. Nonetheless, we show that the parallel MAC game admits a unique
equilibrium almost surely, thus establishing an important class of
counterexamples where these sufficient conditions are not necessary.
Furthermore, if the network's users employ a distributed learning scheme based
on the replicator dynamics, we show that they converge to equilibrium from
almost any initial condition, even though users only have local information at
their disposal.Comment: 18 pages, 4 figures, submitted to Valuetools '1
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