24,708 research outputs found
Bounding Rationality by Discounting Time
Consider a game where Alice generates an integer and Bob wins if he can
factor that integer. Traditional game theory tells us that Bob will always win
this game even though in practice Alice will win given our usual assumptions
about the hardness of factoring.
We define a new notion of bounded rationality, where the payoffs of players
are discounted by the computation time they take to produce their actions. We
use this notion to give a direct correspondence between the existence of
equilibria where Alice has a winning strategy and the hardness of factoring.
Namely, under a natural assumption on the discount rates, there is an
equilibriumwhere Alice has a winning strategy iff there is a linear-time
samplable distribution with respect to which Factoring is hard on average.
We also give general results for discounted games over countable action
spaces, including showing that any game with bounded and computable payoffs has
an equilibrium in our model, even if each player is allowed a countable number
of actions. It follows, for example, that the Largest Integer game has an
equilibrium in our model though it has no Nash equilibria or epsilon-Nash
equilibria.Comment: To appear in Proceedings of The First Symposium on Innovations in
Computer Scienc
Automated Game Design Learning
While general game playing is an active field of research, the learning of
game design has tended to be either a secondary goal of such research or it has
been solely the domain of humans. We propose a field of research, Automated
Game Design Learning (AGDL), with the direct purpose of learning game designs
directly through interaction with games in the mode that most people experience
games: via play. We detail existing work that touches the edges of this field,
describe current successful projects in AGDL and the theoretical foundations
that enable them, point to promising applications enabled by AGDL, and discuss
next steps for this exciting area of study. The key moves of AGDL are to use
game programs as the ultimate source of truth about their own design, and to
make these design properties available to other systems and avenues of inquiry.Comment: 8 pages, 2 figures. Accepted for CIG 201
Simplicity of beliefs and delay tactics in a concession game
I explore the idea of simplicity as a belief-selection criterion in games. A pair of strategies in finite-automata representation (s(1), s(2)) is a Simple Nash Equilibrium (SINE) if: (1) s(j) is a best-reply to s(i); (2) every automaton for player j, which generates the same path as s(j) (given s(i)), has at least as many states as s(j). I apply SINE to a bilateral concession game and show that it captures an aspect of bargaining behavior: players employ delay tactics in order to justify their concessions. Delay tactics are mutually reinforcing, and this may prevent players from reaching an interior agreement. (C) 2003 Elsevier Inc. All rights reserved
Learning to Play Games in Extensive Form by Valuation
A valuation for a player in a game in extensive form is an assignment of
numeric values to the players moves. The valuation reflects the desirability
moves. We assume a myopic player, who chooses a move with the highest
valuation. Valuations can also be revised, and hopefully improved, after each
play of the game. Here, a very simple valuation revision is considered, in
which the moves made in a play are assigned the payoff obtained in the play. We
show that by adopting such a learning process a player who has a winning
strategy in a win-lose game can almost surely guarantee a win in a repeated
game. When a player has more than two payoffs, a more elaborate learning
procedure is required. We consider one that associates with each move the
average payoff in the rounds in which this move was made. When all players
adopt this learning procedure, with some perturbations, then, with probability
1, strategies that are close to subgame perfect equilibrium are played after
some time. A single player who adopts this procedure can guarantee only her
individually rational payoff
Revisiting Synthesis for One-Counter Automata
We study the (parameter) synthesis problem for one-counter automata with
parameters. One-counter automata are obtained by extending classical
finite-state automata with a counter whose value can range over non-negative
integers and be tested for zero. The updates and tests applicable to the
counter can further be made parametric by introducing a set of integer-valued
variables called parameters. The synthesis problem for such automata asks
whether there exists a valuation of the parameters such that all infinite runs
of the automaton satisfy some omega-regular property. Lechner showed that (the
complement of) the problem can be encoded in a restricted one-alternation
fragment of Presburger arithmetic with divisibility. In this work (i) we argue
that said fragment, called AERPADPLUS, is unfortunately undecidable.
Nevertheless, by a careful re-encoding of the problem into a decidable
restriction of AERPADPLUS, (ii) we prove that the synthesis problem is
decidable in general and in N2EXP for several fixed omega-regular properties.
Finally, (iii) we give a polynomial-space algorithm for the special case of the
problem where parameters can only be used in tests, and not updates, of the
counter
- âŠ