Dear philip Ahl,

In a platoon-based driving considering game theory, it is expected that each vehicle selects their strategy without having access to the strategy and without waiting for the decision from other vehicles; i.e., it is a non cooperative and simultaneous game.

According to your question for formulating kindly follow the link below, hope it will beneficial for you.

If you have any other question kindly tell me i will try to help with my best.

Thanks.

https://www.researchgate.net/publication/316463916_A_Game-Theoretic_Approach_and_Evaluation_of_Adversarial_Vehicular_Platooning

Zia Hameed

Thanks for the answer. I think you are right about it being a simultaneous game since at each time step, each vehicle will have to employ some kind of driving strategy, without waiting for other vehicles. But I think the system that I am trying to describe will not be noon-cooperative, but rather cooperative? Correct me if I am wrong. I am thinking that each vehicle shares its optimal trajectory, based on fuel consumption, to each other. Such that if one vehicle notices that its optimal strategy collides with another vehicles optimal strategy, it may give an proposal to that vehicle to change its strategy. The proposal will be external, so is it not a cooperative game?

Zia Hameed

Given the game theoretical classification of this system, how would I prove if there exists a Nash equilibrium to it?

Dear Philip Ahl,

In terms of game theory, if each player has chosen a strategy, and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and their corresponding payoffs constitutes a Nash equilibrium.

Stated simply, Alice and Bob are in Nash equilibrium if Alice is making the best decision she can, taking into account Bob's decision while his decision remains unchanged, and Bob is making the best decision he can, taking into account Alice's decision while her decision remains unchanged. Likewise, a group of players are in Nash equilibrium if each one is making the best decision possible, taking into account the decisions of the others in the game as long as the other parties' decisions remain unchanged.

In game theory, a player's strategy is any of the options which he or she chooses in a setting where the outcome depends not only on their own actions but on the actions of others. A player's strategy will determine the action which the player will take at any stage of the game.

The strategy concept is sometimes (wrongly) confused with that of a move. A move is an action taken by a player at some point during the play of a game (e.g., in chess, moving white's Bishop a2 to b3). A strategy on the other hand is a complete algorithm for playing the game, telling a player what to do for every possible situation throughout the game.

A strategy profile (sometimes called a strategy combination) is a set of strategies for all players which fully specifies all actions in a game. A strategy profile must include one and only one strategy for every player.

The image shown the Nash Equilibrium process.

Hope you understand with it, if you have further query in designing ,feel free to contact me. Thanks

Preprint Strategic Hub-Based Platoon Coordination under Uncertain Travel Times