136,941 research outputs found
Random Numbers and Gaming
In Counter Strike: Global Offensive spray pattern control becomes a muscle memory to a player after long periods of playing. It’s a design choice that makes the gunplay between players more about instant crosshair placement with the faster player usually winning. This is very different from the gunplay of the current popular shooter Player Unknown’s Battlegrounds. Player Unknown’s Battleground’s spray pattern for the guns are random. So how does this affect the player experience? Well as opposed to Counter Strike: Global Offensive, the design choice makes gunplay between two players more about how a person can adapt faster when encountering another. So why does the change from a set pattern to random make for such a different experience in gameplay. Did the usage of randomness make for such a different experience? Random numbers in video games are utilized frequently and have been used for a long time, whether it was better for the player experience is often hard to tell. So just what is this “randomness”? What games use random numbers and why? Are random numbers a bad practice? The usage of random numbers in games is nothing new, but poor implementations and bad business practices have given random numbers a smudge mark on their reputation
On the Convergence Time of the Best Response Dynamics in Player-specific Congestion Games
We study the convergence time of the best response dynamics in
player-specific singleton congestion games. It is well known that this dynamics
can cycle, although from every state a short sequence of best responses to a
Nash equilibrium exists. Thus, the random best response dynamics, which selects
the next player to play a best response uniformly at random, terminates in a
Nash equilibrium with probability one. In this paper, we are interested in the
expected number of best responses until the random best response dynamics
terminates.
As a first step towards this goal, we consider games in which each player can
choose between only two resources. These games have a natural representation as
(multi-)graphs by identifying nodes with resources and edges with players. For
the class of games that can be represented as trees, we show that the
best-response dynamics cannot cycle and that it terminates after O(n^2) steps
where n denotes the number of resources. For the class of games represented as
cycles, we show that the best response dynamics can cycle. However, we also
show that the random best response dynamics terminates after O(n^2) steps in
expectation.
Additionally, we conjecture that in general player-specific singleton
congestion games there exists no polynomial upper bound on the expected number
of steps until the random best response dynamics terminates. We support our
conjecture by presenting a family of games for which simulations indicate a
super-polynomial convergence time
When Can Limited Randomness Be Used in Repeated Games?
The central result of classical game theory states that every finite normal
form game has a Nash equilibrium, provided that players are allowed to use
randomized (mixed) strategies. However, in practice, humans are known to be bad
at generating random-like sequences, and true random bits may be unavailable.
Even if the players have access to enough random bits for a single instance of
the game their randomness might be insufficient if the game is played many
times.
In this work, we ask whether randomness is necessary for equilibria to exist
in finitely repeated games. We show that for a large class of games containing
arbitrary two-player zero-sum games, approximate Nash equilibria of the
-stage repeated version of the game exist if and only if both players have
random bits. In contrast, we show that there exists a class of
games for which no equilibrium exists in pure strategies, yet the -stage
repeated version of the game has an exact Nash equilibrium in which each player
uses only a constant number of random bits.
When the players are assumed to be computationally bounded, if cryptographic
pseudorandom generators (or, equivalently, one-way functions) exist, then the
players can base their strategies on "random-like" sequences derived from only
a small number of truly random bits. We show that, in contrast, in repeated
two-player zero-sum games, if pseudorandom generators \emph{do not} exist, then
random bits remain necessary for equilibria to exist
Efficient winning strategies in random-turn Maker-Breaker games
We consider random-turn positional games, introduced by Peres, Schramm,
Sheffield and Wilson in 2007. A -random-turn positional game is a two-player
game, played the same as an ordinary positional game, except that instead of
alternating turns, a coin is being tossed before each turn to decide the
identity of the next player to move (the probability of Player I to move is
). We analyze the random-turn version of several classical Maker-Breaker
games such as the game Box (introduced by Chv\'atal and Erd\H os in 1987), the
Hamilton cycle game and the -vertex-connectivity game (both played on the
edge set of ). For each of these games we provide each of the players with
a (randomized) efficient strategy which typically ensures his win in the
asymptotic order of the minimum value of for which he typically wins the
game, assuming optimal strategies of both players.Comment: 20 page
Statistical mechanics of random two-player games
Using methods from the statistical mechanics of disordered systems we analyze
the properties of bimatrix games with random payoffs in the limit where the
number of pure strategies of each player tends to infinity. We analytically
calculate quantities such as the number of equilibrium points, the expected
payoff, and the fraction of strategies played with non-zero probability as a
function of the correlation between the payoff matrices of both players and
compare the results with numerical simulations.Comment: 16 pages, 6 figures, for further information see
http://itp.nat.uni-magdeburg.de/~jberg/games.htm
Random multi-player games
The study of evolutionary games with pairwise local interactions has been of interest to many different disciplines. Also, local interactions with multiple opponents had been considered, although always for a fixed amount of players. In many situations, however, interactions between different numbers of players in each round could take place, and this case cannot be reduced to pairwise interactions. In this work, we formalize and generalize the definition of evolutionary stable strategy (ESS) to be able to include a scenario in which the game is played by two players with probability p and by three players with the complementary probability 1-p. We show the existence of equilibria in pure and mixed strategies depending on the probability p, on a concrete example of the duel-truel game. We find a range of p values for which the game has a mixed equilibrium and the proportion of players in each strategy depends on the particular value of p. We prove that each of these mixed equilibrium points is ESS. A more realistic way to study this dynamics with high-order interactions is to look at how it evolves in complex networks. We introduce and study an agent-based model on a network with a fixed number of nodes, which evolves as the replicator equation predicts. By studying the dynamics of this model on random networks, we find that the phase transitions between the pure and mixed equilibria depend on probability p and also on the mean degree of the network. We derive mean-field and pair approximation equations that give results in good agreement with simulations on different networks.Fil: Kontorovsky, Natalia Lucía. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaFil: Pinasco, Juan Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Vazquez, Federico. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentin
Noncooperative Bargaining in Apex Games and the Kernel
This paper studies non-cooperative bargaining with random proposers in apex games. Two di¤erent protocols are considered: the egalitarian propocol, which selects each player to be the proposer with the same probability, and the proportional protocol, which selects each player with a probability proportional to his number of votes. Expected equilibrium payo¤s coincide with the kernel for the grand coalition regardless of the protocol. Expected payo¤s conditional on a coalition may depend on the protocol: given a coalition of the apex player with a minor player, an egalitarian protocol yields a nearly equal split whereas a proportional protocol leads to a proportional split.noncooperative bargaining;apex games;kernel;random proposers
Infinite-Duration Bidding Games
Two-player games on graphs are widely studied in formal methods as they model
the interaction between a system and its environment. The game is played by
moving a token throughout a graph to produce an infinite path. There are
several common modes to determine how the players move the token through the
graph; e.g., in turn-based games the players alternate turns in moving the
token. We study the {\em bidding} mode of moving the token, which, to the best
of our knowledge, has never been studied in infinite-duration games. The
following bidding rule was previously defined and called Richman bidding. Both
players have separate {\em budgets}, which sum up to . In each turn, a
bidding takes place: Both players submit bids simultaneously, where a bid is
legal if it does not exceed the available budget, and the higher bidder pays
his bid to the other player and moves the token. The central question studied
in bidding games is a necessary and sufficient initial budget for winning the
game: a {\em threshold} budget in a vertex is a value such that
if Player 's budget exceeds , he can win the game, and if Player 's
budget exceeds , he can win the game. Threshold budgets were previously
shown to exist in every vertex of a reachability game, which have an
interesting connection with {\em random-turn} games -- a sub-class of simple
stochastic games in which the player who moves is chosen randomly. We show the
existence of threshold budgets for a qualitative class of infinite-duration
games, namely parity games, and a quantitative class, namely mean-payoff games.
The key component of the proof is a quantitative solution to strongly-connected
mean-payoff bidding games in which we extend the connection with random-turn
games to these games, and construct explicit optimal strategies for both
players.Comment: A short version appeared in CONCUR 2017. The paper is accepted to
JAC
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