This paper presents a novel learning framework to provide computer game agents the ability to adapt to the player as well as other game agents. Our technique generally involves a personality adaptation module encapsulated in a reinforcement learning framework. Unlike previous work in which adaptation normally involves a decision process on every single action the agent takes, we introduce a two-level process whereby adaptation only takes place on an abstracted actions set which we coin as agent personality. With the personality defined, each agent will then take actions according to the restrictions imposed in its personality. In doing so, adaptation takes place in appropriately defined intervals in the game, without disrupting or slowing down the game constantly with intensive decision-making computations, hence improving enjoyment for the player. Moreover, by decoupling adaptation from action selection, we have a modular adaptive system that can be used with existing action planning methods. With an actual typical game scenario that we have created, it is shown that a team of agents using our framework to adapt towards the player are able to perform better than a team with scripted behavior. Consequently, we also show the team performs even better when adapted towards each other.