In other words, in what conditions the game theory is better than conventional optimization methods for solving optimization problems?
Game theory is used to analyze situations where we have interdependence among the players. But optimization may not always pertain to interdependence among the agents. For example, optimization in oligopoly models involve computation of Nash equilibrium. Lastly, Nash equilibrium may not always be Pareto optimal.
Thank you Dr. Sanyal for your response. I got you. In cooperative games, can we say that both methods are equally applicable and produce similar results?
It is indeed my pleasure to interact with you Sir. In cooperative games, I believe yes.
I think it helps to distinguish between "decision situations" and "decision mechanisms". Your question is more about the situation than the mechanism. Imagine asking, "what is the nash equilibrium solution to strength maximizing shape of a beam?" It is the exact same solution as any conventional optimizing method would generate.
What is called conventional in the question probably means "Given an opportunity set, select the best". This is a mechanism.
A Nash equilibrium also does this, but it does something else before it "selects the best". First it figures out, given the specific situation, what is in fact the opportunity set. In game theory, this is the "core" and it represents the set of stable equilibria. If the core was mathematically ill-behaved, like most phisical problems are, then one might try eloborate "guess and check" routines like generic algorythms to figure out what is the best opportunity within the core. That is, with respect to the core, one solves a Nash Equilibrium just like the conventional problems.
The situations that call for game theory methods are ones where the opportunity set depends on my choice in a very specific way. The Hotelling "hotdog stand on the beach" problem illustrates this quite well. My initial assesment of opportunities along the beach are not those that I actually get, because the true opportunites depend on what I choose. In fact, it depends on my strategy and my opponent's strategy. The physical world typically does not present researchers with this kind of decision situation.
Here is one where it does: What is the cost minimizing combinations of intervention strategies when multiple infrastructure networks overlap? The opportunity set depends on the choices.
In the paper:
On the Computation of Nash and Pareto Equilibria for Some Bi-objective Control Problems,
some theoretical and computational results are presented.
https://www.researchgate.net/publication/325782636_On_the_Computation_of_Nash_and_Pareto_Equilibria_for_Some_Bi-objective_Control_Problems/stats
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