Abstract |
Industrial processes and research activities quite often involve interactions between selfinterested participants. Game theory is a standard tool to analyze and study these interactions,
but usually comes along with the assumption that the participants (i.e. agents, players) have
a common and correct (albeit not always complete) knowledge with regards to the abstract
formulation of the interaction. However, in many real-world situations, it could be the case
that (some of) the agents are misinformed with regards to the game that they play, essentially
having an incorrect understanding of the setting, without being aware of it. This would
invalidate the common knowledge assumption. To study this phenomenon in this dissertation
we establish a new framework.
We initiate our study by presenting a new game-theoretic framework, called misinformation
games, that provides the formal machinery necessary to study this phenomenon, and present
some basic results regarding its properties. Interestingly, the new concept provides new
equilibrium concepts, related to the Nash equilibrium. Thereupon, we introduce a new metric,
called Price of Misinformation, in order to quantify the influence of misinformation in the
efficiency of the interaction. Furthermore, we apply our framework in a variety of well-known
classes of games.
Afterwards, we expand the misinformation game model, by developing a discrete-time
iterative procedure, where in each time step each agent chooses an action according to the
(possibly erroneous) game specification that she possesses. Then, the actual payoffs that
correspond to the agglomeration of the agents’ choices are publicly announced, thus allowing
agents to update their information. Consequently, agents may re-evaluate their behaviour in
the next time step. We call this process Adaptation Procedure, and we provide various results
regarding its properties. Further, we present a complete analysis of the behaviour of the
agents as their game specifications are updated, and show that this leads to new equilibrium
concepts.
Thereafter, we enrich the Adaptation Procedure by incorporating the epistemic view
that each agent has regarding the interaction. Towards this direction, we formally define
the epistemic perspective of Adaptation Procedure in misinformation games. Namely, we
construct a process, called Epistemic Adaptive Evolution, where agents revise both their
information and their epistemic knowledge according to the game they play. This also provides
new equilibrium concepts. With this at hand, we complete our framework, through which we
can study the phenomenon of agent interaction with incorrect information.
Evidently, in several cases in our model, it is necessary to compute several equilibrium
concepts. For that, we introduce a novel online learning algorithm. Specifically, we propose a
novel variant of the multiplicative weights update method using best-response strategies, that
guarantees last-iterate convergence for zero-sum games with a unique Nash equilibrium.
Next, we consider the case of misinformation games where the misinformation is due
to random noise that additively distorts the payoff matrices of the agents (e.g., due to
communication errors). We call this setting noisy games. We analyze the general properties
of two-players noisy games and we derive theoretical formulas which determine the probability
that the noise will significantly affect the strategic behaviour of the agents, based on the noise
intensity and pattern.
Following the analysis and study of interaction from the perspective of the participants, we
approach the problem from the perspective of the game’s designer. In particular, we introduce
a novel approach for Coordination mechanisms in games, based on the idea of misinforming
agents about the game formulation, in order to steer them towards a behaviour that leads to
an improved outcome in terms of social welfare. We propose a mechanism that provides the
agents with the right incentives to adopt a socially optimal behaviour by misinforming them.
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