Cheating in adaptive games motivated by electricity markets

We study Dynamic Game situations with incomplete structural information, motivated by problems arising in electricity market modeling. Some Adaptive strategies are considered as an expression of the Bounded Rationality of the participants of the game. The Adaptive strategies are typically not in Nash equilibrium. Thus, in order to assess those strategies, two criteria are stated: Firstly, how far the cost of each player is from the cost of her best response in the sense of the Nash equilibrium. Secondly, we consider the case where the first player follows the adaptive strategy and the second player implements the best response to the first player. Then, the criterion depends on the difference of the cost of the first player comparing with the cost in case where both players follow their adaptive control laws. This difference may be positive or negative. We then examine a smaller class of strategies, called the pretender strategies, where each player acts as if she had different, not real, preferences. It turns out that under certain technical conditions, if only one player is pretending, she can achieve the same cost as if she were Stackelberg leader. The situation where all the players are pretending is then considered. The effects of adaptation and cheating, when the number of players in the game becomes large, is examined in a simple example.