# 代写project | Objective – prj

### Compact ordered space II (required)

#### Two examples:

(^1) A bounded and closed interval. (^2) A finite set equipped with any order. Every function on a finite set is

#### Two properties:

(^1) Every closed subset of a compact ordered space has a greatest

#### element and a smallest element.

(^2) Every monotone sequence in a compact ordered space has a limit.

### Topkiss Theorem for compact ordered spaces

#### is continuous in x for every T. Then the following are true.

(^1) For every T, f (,) has a maximum; in fact, the set of maxima of

#### f (,) has a largest element x () and a smallest element x ().

(^2) For , T with , x () x () and x () x ().

### Common knowledge

#### Informally, something is a common knowledge if

(^1) Everybody knows it. (^2) Everybody knows that everybody knows it. (^3) Everybody knows that everybody knows that everybody knows it. (^4) …

### Guessing 2/3 of the average

(^) s

#### s

(^) , where s = n ^1

### Definition

#### following two cases:

(^1) Si is a bounded and closed interval and ui is continuous. (^2) Si is a finite set.

### The main theorem

#### The following is true for a supermodular game.

(^1) For every player i N, there exists a smallest rationalizable strategy s

#### and a greatest rationalizable strategy si.

(^2) sand s are Nash equilibria.