Rigorous Theories of Business Strategies in a World of Evolving Knowledge - Topics day 2

Strategy theory adopted the tool of game theory to model the interaction of firms. However, game theory needs to be extended to account for situations in which the abilities of the involved players to imagine the consequences of particular actions differ. There are promising formal structures with which we believe this goal can be achieved, prominently games with unawareness structures. However, to successfully apply game theory to situations in which the interaction among firms first shapes a new business environment, we need to resolve some important, and difficult, conceptual questions.
Perhaps most generally spoken, games with unawareness allow to express that different players reason using different descriptions of the world. In the real world, a puzzling question is 'how language shapes interaction'. If games with unawareness are an adequate tool to express how language shapes interaction is a question that needs attention. A related conceptual questions is how (if at all) the differences in the imagination of possibilities of interacting players can be accounted for using unawareness structures.
And how do differences in the awareness of interacting firms relate to competitive advantages? Recently, in the strategy field, it has been discussed if differences in the languages (more precisely: differences in the abilities to represent a strategic problem) of interacting firms can account for superior decision-making (Brandenburger and Vinokurova, 2011).
But how exactly do superior cognitive abilities (judged by strategic success) relate to differences in the languages of firms?
We wish to discuss the following questions in a systematic manner during the workshop:

1. How do differences in imagination among decision-makers relate to differences in their language ?
2. How can differences in languages  and imagination be modeled using awareness/ unawareness structures? For instance, how does, if at all, the richness of a strategic vocabulary correspond to the richness of a state space of a player with particular awareness?

Moreover, we need to make assumptions how both awareness and beliefs change over time in the course of interaction. How does the awareness of players change over time in the real world? What are systematic rules of awareness change that we can build into games with unawareness?
A related question is what a player should do (from a normative perspective) if he arrives at a situation in a game in which he cannot rationalize the actions of the other players, i.e. where the moves of the opponents cannot be explained as best responses, given the player's awareness and beliefs about the game. This player could conclude that the other players are not rational. But does such conclusion really make sense in a world of radically incomplete knowledge?
The decision maker may rather think: My opponents must be aware of something that I am not aware off, and this rationalizes their behavior. But how does 'something that I do not know but that must exist' enter the formal knowledge base of a decision-maker? Rather than approaching this problem from theory, we should introspect how we as smart humans deal with such problems in our real strategic interactions, and then project our introspection to the formal structures we are developing.
Games with unawareness have the potential to make our understanding how competitive advantages come about more precise. For instance, the value of certain resources may first emerge in and hinges upon the course of interaction among firms. Unawareness structures may be helpful to describe the properties of such interactions.
Just think of the resource that Apple gained from contracting with the music publishers in 2002. As a consequence of the contract with the publishers, it owned an online music portal offering songs from all five major publishers, and a compatible music device. The publishers believed that the potential value of this resource (that Apple gained by making the contract with them) has an upper bound, as Apple computers' market share was small in 2002, and the contract was restricted to selling songs that can be played exclusively on Apple computers and Apple devices. But they did not think about the possibility that the existence of this resource may dramatically increase the market share of Apple in both music and computer markets. Thus, the reflexive interaction between actions that shape a business field and the value of resources in this field was not paid attention to by the publishers.
Games with unawareness may help to analyze such situations, as they allow to model that one party can foresee consequences of actions that the other party doesn't see.