There is also uncertainty about Firm I's beliefs-but in a degenerate sense: there is a one-one relationship between Player 1s conditional beliefs at any w Q and her cost At first blush, this makes sense: after all, payoff uncertainty is about Player 1s cost, so as soon as Firm 1 learns the value of c, her uncertainty is resolved. Similarly, since Firm 2s cost is known to be zero, there is no payoff uncertainty as far as the latter is concerned. How about the absence of uncertainty about Firm 2s beliefs? This is a legitimate as sumption, of course. The point is, it is only an assumption: it is not a necessary consequence of rationality, of the Bayesian approach, or, indeed, a necessary feature of Harsanyi's model of incomplete information "Unconventional""(but legit)use of Harsanyi's approach Indeed, it is very easy to enrich the model to allow for uncertainty (on Firm 1's part)about Firm 2s beliefs Let us consider the following alternative model for our Cournot game. First, Q=wary E 10, 5:a,y E(1, 2. The interpretation is that in state wary, Firm 1's cost is c,Firm 1’s" belief state”isr, and firm2s“ belief state”isgy. This terminology is nonstandard and merely suggestive: the exact meaning will be clear momentarily Next,letn1={{ual,uc}:c∈{0,},x∈{1,2}}={:c∈{0,是},x∈{1,2}and I learns her cost and bewley]: yE11, 2))=(t2: y E(1, 2). Thus, at each state w, Firm T2={t er“ belief state”, and firn2 learns his“ belief state We can get a lot of action from this simple extension. Let us define conditional proba- bilities as follow P2(uon|+2)=p2(u21+)=0.5 i. e. type t) of Firm 2 is certain that Firm 1 is in belief state I whenever her cost is 0,in belief state 2 whenever her cost is 2; moreover, the two combinations of belief states and costs are equally likely. Next p2(ai212)=1-p2(22)=075 i.e. t2 is certain that Firm 1s belief state, regardless of cost, is 3= 2; moreover, he has a different marginal on c than type t). Finally n(cn()=p1(a14)=1andp1a)=ph(un142)=1 that is, regardless of her cost, in belief state 1 Firm 1 is certain that she is facing type t? hereas in belief state 2 she considers both types of Firm 2 to be equally likely. As I noted last time, this is really not relevant(also see the "Common priors"section below) To complete the specification of our priors, we simply assume that players regard the cells of their respective type partitions as being equally likelyThere is also uncertainty about Firm 1’s beliefs—but in a degenerate sense: there is a one-one relationship between Player 1’s conditional beliefs at any ω ∈ Ω and her cost. At first blush, this makes sense: after all, payoff uncertainty is about Player 1’s cost, so as soon as Firm 1 learns the value of c, her uncertainty is resolved. Similarly, since Firm 2’s cost is known to be zero, there is no payoff uncertainty as far as the latter is concerned. How about the absence of uncertainty about Firm 2’s beliefs? This is a legitimate as￾sumption, of course. The point is, it is only an assumption: it is not a necessary consequence of rationality, of the Bayesian approach, or, indeed, a necessary feature of Harsanyi’s model of incomplete information. “Unconventional” (but legit) use of Harsanyi’s approach Indeed, it is very easy to enrich the model to allow for uncertainty (on Firm 1’s part) about Firm 2’s beliefs. Let us consider the following alternative model for our Cournot game. First, Ω = {ωcxy : c ∈ {0, 1 2 }; x, y ∈ {1, 2}}. The interpretation is that in state ωcxy, Firm 1’s cost is c, Firm 1’s “belief state” is x, and Firm 2’s “belief state” is y. This terminology is nonstandard and merely suggestive: the exact meaning will be clear momentarily. Next, let T1 = {{ωcx1, ωcx2} : c ∈ {0, 1 2 }, x ∈ {1, 2}} = {t cx 1 : c ∈ {0, 1 2 }, x ∈ {1, 2}} and T2 = {{ω01y, ω02y, ω 1 2 1y , ω 1 2 2y} : y ∈ {1, 2}} = {t y 2 : y ∈ {1, 2}}. Thus, at each state ω, Firm 1 learns her cost and her “belief state”, and Firm 2 learns his “belief state.” We can get a lot of action from this simple extension. Let us define conditional proba￾bilities as follows: p2(ω011|t 1 2 ) = p2(ω 1 2 21|t 1 2 ) = 0.5 i.e. type t 1 2 of Firm 2 is certain that Firm 1 is in belief state 1 whenever her cost is 0, in belief state 2 whenever her cost is 1 2 ; moreover, the two combinations of belief states and costs are equally likely. Next, p2(ω022|t 2 2 ) = 1 − p2(ω 1 2 22|t 2 2 ) = 0.75 i.e. t 2 2 is certain that Firm 1’s belief state, regardless of cost, is x = 2; moreover, he has a different marginal on c than type t 1 2 . Finally, p1(ω011|t 01 1 ) = p1(ω 1 2 11|t 1 2 1 1 ) = 1 and p1(ω021|t 02 1 ) = p1(ω 1 2 21|t 1 2 2 1 ) = 1 2 that is, regardless of her cost, in belief state 1 Firm 1 is certain that she is facing type t 1 2 , whereas in belief state 2 she considers both types of Firm 2 to be equally likely. As I noted last time, this is really not relevant (also see the “Common priors” section below). To complete the specification of our priors, we simply assume that players regard the cells of their respective type partitions as being equally likely. 3