Yep, a game of complete information is just one is which the structure of the game is known to all players. When wikipedia says
The utility functions (including risk aversion), payoffs, strategies and “types” of players are thus common knowledge.
it’s an unfortunately ambiguous phrasing but it means
The specific utility function each player has, the specific payoffs each player would get from each possible outcome, the set of possible strategies available to each player, and the set of possible types each player can have (e.g. the set of hands they might be dealt in cards) are common knowledge.
It certainly does not mean that the actual strategies or source code of all players are known to each other player.
Well in that case classical game theory doesn’t seem up to the task, since in order to make optimal decisions you’d need a probability distribution over the opponent’s strategies, no?
Right, vanilla game theory is mostly not a tool for making decisions.
It’s about studying the structure of strategic interactions, with the idea that some kind of equilibrium concept should have predictive power about what you’ll see in practice. On the one hand, if you get two humans together and tell them the rules of a matrix game, Nash equilibrium has relatively little predictive power. But there are many situations across biology, computer science, economics and more where various equilibrium concepts have plenty of predictive power.
Yep, a game of complete information is just one is which the structure of the game is known to all players. When wikipedia says
it’s an unfortunately ambiguous phrasing but it means
It certainly does not mean that the actual strategies or source code of all players are known to each other player.
Well in that case classical game theory doesn’t seem up to the task, since in order to make optimal decisions you’d need a probability distribution over the opponent’s strategies, no?
Right, vanilla game theory is mostly not a tool for making decisions.
It’s about studying the structure of strategic interactions, with the idea that some kind of equilibrium concept should have predictive power about what you’ll see in practice. On the one hand, if you get two humans together and tell them the rules of a matrix game, Nash equilibrium has relatively little predictive power. But there are many situations across biology, computer science, economics and more where various equilibrium concepts have plenty of predictive power.
But doesn’t the calculation of those equilibria require making an assumption about the opponent’s strategy?