319 research outputs found
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
Fashion, Cooperation, and Social Interactions
Fashion plays such a crucial rule in the evolution of culture and society
that it is regarded as a second nature to the human being. Also, its impact on
economy is quite nontrivial. On what is fashionable, interestingly, there are
two viewpoints that are both extremely widespread but almost opposite:
conformists think that what is popular is fashionable, while rebels believe
that being different is the essence. Fashion color is fashionable in the first
sense, and Lady Gaga in the second. We investigate a model where the population
consists of the afore-mentioned two groups of people that are located on social
networks (a spatial cellular automata network and small-world networks). This
model captures two fundamental kinds of social interactions (coordination and
anti-coordination) simultaneously, and also has its own interest to game
theory: it is a hybrid model of pure competition and pure cooperation. This is
true because when a conformist meets a rebel, they play the zero sum matching
pennies game, which is pure competition. When two conformists (rebels) meet,
they play the (anti-) coordination game, which is pure cooperation. Simulation
shows that simple social interactions greatly promote cooperation: in most
cases people can reach an extraordinarily high level of cooperation, through a
selfish, myopic, naive, and local interacting dynamic (the best response
dynamic). We find that degree of synchronization also plays a critical role,
but mostly on the negative side. Four indices, namely cooperation degree,
average satisfaction degree, equilibrium ratio and complete ratio, are defined
and applied to measure people's cooperation levels from various angles. Phase
transition, as well as emergence of many interesting geographic patterns in the
cellular automata network, is also observed.Comment: 21 pages, 12 figure
A Model of Noisy Introspection
This paper presents a theoretical model of noisy introspection designed to explain behavior in games played only once. The equilibrium determines layers of beliefs about others' beliefs about ..., etc., but allows for surprises by relaxing the equilibrium requirement that belief distributions coincide with decision distributions. The paper contains a convergence proof and reports estimated introspection and error parameters for data from 37 one-shot matrix games. The accuracy of the model is compared with that of two alternative approaches: the Nash equilibrium and the logit quantal response equilibrium.game theory, introspection, Nash equilibrium, experiments.
Using Games to Understand and Create Randomness
Massive growth of data and communication encryption has created growing need for non-predictable, random data, needed for encryption keys creation. Need for randomness grows (nearly) linearly with growth of encryption, but randomness is very important ingredient also e.g. in quickly growing industry of game programming. Computers are deterministic devices and cannot create random results, computer procedures can generate only pseudo-random (looking random) data. For true randomness is needed some outside information - time and placement of user's keystrokes, fluctuations of current, interrupt requests in computer processor etc. But even those sources can often not comply with requests from our increasingly randomness-hunger environment of ciphered communications and data. Growing need for randomness has created a market of randomness sources; new sources are proposed constantly. These sources differ in their properties (ease of access, size of required software etc.) and in ease of estimating their quality. However, there is an easily available good source for comparing quality of randomness and also creating new randomness - computer games. The growing affectionateness of users to play digital games makes this activity very attractive for comparing quality of randomness sources and using as a source of new randomness. In the following are analyzed possibilities for investigating and extracting randomness from digital gameplay and demonstrated some experiments with simple stateless games which allow to compare existing sources of (pseudo) randomness and generate new randomness, which can be used e.g. to create cyphering keys in mobile and Internet of Things devices.publishedVersionPeer reviewe
Different impressions of other agents obtained through social interaction uniquely modulate dorsal and ventral pathway activities in the social human brain
Internal (neuronal) representations in the brain are modified by our experiences, and this phenomenon is not unique to sensory and motor systems. Here, we show that different impressions obtained through social interaction with a variety of agents uniquely modulate activity of dorsal and ventral pathways of the brain network that mediates human social behavior.
We scanned brain activity with functional magnetic resonance imaging (fMRI) in 16 healthy volunteers when they performed a simple matching-pennies game with a human, human-like android, mechanical robot, interactive robot, and a computer. Before playing this game in the scanner, participants experienced social interactions with each opponent separately and scored their initial impressions using two questionnaires.
We found that the participants perceived opponents in two mental dimensions: one represented âmind-holdernessâ in which participants attributed anthropomorphic impressions to some of the opponents that had mental functions, while the other dimension represented âmind-readernessâ in which participants characterized opponents as intelligent. Interestingly, this âmind-readernessâ dimension correlated to participants frequently changing their game tactic to prevent opponents from envisioning their strategy, and this was corroborated by increased entropy during the game. We also found that the two factors separately modulated activity in distinct social brain regions. Specifically, mind-holderness modulated activity in the dorsal aspect of the temporoparietal junction (TPJ) and medial prefrontal and posterior paracingulate cortices, while mind-readerness modulated activity in the ventral aspect of TPJ and the temporal pole.
These results clearly demonstrate that activity in social brain networks is modulated through pre-scanning experiences of social interaction with a variety of agents. Furthermore, our findings elucidated the existence of two distinct functional networks in the social human brain. Social interaction with anthropomorphic or intelligent-looking agents may distinctly shape the internal representation of our social brain, which may in turn determine how we behave for various agents that we encounter in our society
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