Chapter 1 How do agents represent? Alex Ryan DSTO, Australia alex.ryan@dsto.defence.gov.au Representation is inherent to the concept of an agent, but its importance in complex systems has not yet been widely recognised. In this paper I introduce Peirce’s theory of signs, which facilitates a definition of representation in general. In summary, repres- entation means that for some agent, a model is used to stand in for another entity in a way that shapes the behaviour of the agent with respect to that entity. Representation in general is then related to the theories of representation that have developed within different disciplines. I compare theories of representation from metaphysics, military theory and systems theory. Additional complications arise in explaining the special case of mental representations, which is the focus of cognitive science. I consider the dominant theory of cognition – that the brain is a representational device – as well as the sceptical anti-representational response. Finally, I argue that representation distinguishes agents from non-representational objects: agents are objects capable of representation. 1.1 Introduction Representation is an essential concept for understanding the behaviour of agents in a complex system. Consider traders in a stock exchange market as agents. If every agent has unmediated access to the value of a company (including its exact future profits discounted to present value), then the market cannot exist, since shareholders would only be willing to sell above this value, a price no rational buyer would pay 1 . Only when partial information on value is allowed 1 One might expect trades to be made exactly at the value of the stock. However, once a financial or time cost is included no rational buyer can exist. Why would an agent buy shares that never increase in real value and incur an exit fee?