Problems (or games) involving several agents (or players) where the decisions (or strategies) of one of them affect the rest and vice versa are very common in economics. Game theory is the theory in charge of studying this type of situation. We distinguish several types of games: collaborative, where players act in search of a common reward; and competitive, where players act in search of their own reward. Within competitive games we distinguish, in turn, zero-sum games, where players who win do so at the expense of those who lose; and non-zero-sum games, where a player can change his strategy to improve his situation without worsening that of the others, or even improving the situation of the others as well. In game theory, concepts such as Nash Equilibrium and Pareto Optimality are of great relevance. In non-zero-sum competitive games, situations such as the famous Prisoner's Dilemma can occur, which raises interesting questions about the individual good and the common good. Gate-based quantum computation, through phenomena such as superposition or entanglement, offers novel answers to such dilemmas. While it is a theory that presents significant challenges, it also has great potential. It should be noted that quantum game theory is QETEL's most theoretical line of research. You can find more information in our white paper.
In this blog we show the results of a method that consists of introducing the possibility that in an iterative game each player can adjust the parameters of their quantum plays iteratively to optimise their own payoff through a cost function using, for example, gradient descent techniques.
In a previous QETEL blog post we talked about the Braess Paradox and some related ideas such as Game Theory or Nash Equilibrium. However, we did not explain what Quantum Game Theory is and why it can achieve better results. To do so, we will fix ideas by reasoning with a concrete game and a particular quantization scheme.
We have all experienced the effect of traffic congestion on the road at one time or another. We have lost time, become angry and perhaps, in desperation, demanded that new roads be built. However, did you know that building new roads can lead to more congestion and increased travel time? This counter-intuitive fact is known as the Braess's paradox.