In mechanism design theory we take a normative stance, aiming to produce a certain 'wanted' state, constructing the potential strategies we provide, and the rules we formulate, and letting the mechanism do the rest.
The overall logic behind the mechanism is simple. We have apriori options, and we have preferences over those choices, where each player is not aware of his state at the moment, very similar to Rawls veil of ignorance.
Before ever knowing who he would be in the game, each player provides preferences over all possible options and what strategies he would take at each player state.
The beauty here is that, if we as a family agree upon a certain mechanism before we ever know who we shall be at game time, we get an all agree-all fair game, where each player gets the maximal individual utility.
It is interesting to examine this specific notion of a game from two different perspectives.
First, if we take each player i, out of N players, and we provided him with every possible player-state and strategy, we can aggregate N player's decisions and see what we would like to have at the terminal node (final result). This is not a complete utility maximizer because we aggregate, thus there are times when each player wants the same as the others, and times that does not happen.
Second, we can take a central planner, similar to the SSR for example, and decide on a result we would like to get, construct a game with rules that each player must go by, and let the mechanism run. This is of course spectacular from the central planner prism.
Another very interesting cross-section we can examine is the environment of bayesian statistics and the First above-mentioned option. Here, constructing strategies is a bit harder, and aggregating is even tougher now because each player now has some bayesian belief about his or her player-state. Here, we can have delusional players thinking that once we unveil the curtain they will be surprised to find they are not in the place they thought they will be, and we can have very bad results regarding the design of a unified mechanism.
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