$\begin{array}{c} \mathop {Max}\limits_{\scriptstyle {\rm{\lambda }}_{\rm{R}} {\rm{, \lambda }}_{\rm{B}} {\rm{, \lambda }}_{\rm{M}} {\rm{,}} \atop \scriptstyle {\rm{\sigma }}_{{\rm{1B}}} {\rm{, \sigma }}_{{\rm{1M}}} {\rm{, \sigma }}_{{\rm{2B}}} {\rm{, \sigma }}_{{\rm{2M}}} } \pi = P_L \left( {\sigma _{LB} + \sigma _{LM} + \Sigma _{ - L} } \right)(\sigma _{LB} + \sigma _{LM} ) - C_B \sigma _{LB} - C_M \sigma _{LM} \\ + P_H \left( {\sigma _{HB} + \sigma _{HM} + \Sigma _{ - H} } \right)(\sigma _{HB} + \sigma _{HM} ) - C_B \sigma _{HB} - C_M \sigma _{HM} \\ + \lambda _R r - \lambda _B F_B - \lambda _M F_M \\ \end{array}$

$\lambda _R^* = \Lambda - \frac{{(\alpha - C_M )}}{{(N + 1)\beta }}F_B - \frac{{\left( {\varepsilon - F_M (1 + r)} \right)}}{{(N + 1)\beta }}F_M - \frac{{\left\{ {2(C_M - C_B ) - (F_B - F_M )} \right\}}}{{(N + 1)\beta }}(F_B - F_M )$

$\int\limits_0^{\sigma _{LB} + \sigma _{LM} } {P_L \left( \sigma \right)d\sigma } + \int\limits_0^{\sigma _{HB} + \sigma _{HM} } {P_H \left( \sigma \right)d\sigma } - C_B \left( {\sigma _{LB} + \sigma _{HB} } \right) - C_M \left( {\sigma _{LM} + \sigma _{HM} } \right) + \lambda _R r - \lambda _B F_B - \lambda _M F_M$

Figure 3 displays the cycling of both outputs and prices in Session 4 around the Cournot benchmarks for both Markets L and H. Price is plotted against the axis on the left, and output is plotted against the axis to the right. A single, horizontal line indicates the Cournot benchmark of (price, output) = (200, 24) for Market H, and a single dashed line indicates the Cournot benchmark of (100, 18) for Market L. The time series of both prices and outputs do not "converge" to the benchmarks, although they do line up with the benchmarks at different times during the session. What is striking, however, are not the time series but the averages of these quantities, especially the averages of the outputs.

Figure 4 shows the decline in producer surplus over time to the Social Optimum level (the dashed line). It then oscillates in a single period between the Social Optimum and Cournot benchmarks, recalling a "sawtooth pattern." Retail Gasoline markets operate in such a manner, with the rate of increase far exceeding the succeeding rate of decline to previous levels.

Figure 5 shows total surplus and consumer surplus in six experimental sessions. In the first three sessions, the consumer surplus level realized in the experiment oscillates above and below the theoretical level of consumer surplus that would be realized in a Cournot game. Total surplus achieved, however, is very close the theoretical total surplus expected from a Cournot setting. In the last three sessions, the Cournot and total surplus levels are markedly higher than the first three sessions, and the realized consumer surplus continues to range above and below the theoretical prediction. Total suplus, however, appears to fall short of the Cournot level more often than under the previous treatment condition.

$\begin{array}{c} L = P_L \left( {\sigma _{LB} + \sigma _{LM} + \Sigma _{ - L} } \right)(\sigma _{LB} + \sigma _{LM} ) - C_B \sigma _{LB} - C_M \sigma _{LM} \\ + P_H \left( {\sigma _{HB} + \sigma _{HM} + \Sigma _{ - H} } \right)(\sigma _{HB} + \sigma _{HM} ) - C_B \sigma _{HB} - C_M \sigma _{HM} \\ + \lambda _R r - \lambda _B F_B - \lambda _M F_M \\ + \mu (\Lambda - \lambda _R - \lambda _B F_B - \lambda _M F_M ) \\ + \mu _R \lambda _R + \mu _B \lambda _B + \mu _M \lambda _M \\ + \mu _{LB} (\lambda _B - \sigma _{LB} ) + \mu _{LM} (\lambda _M - \sigma _{LM} ) + \mu _{HB} (\lambda _B - \sigma _{HB} ) + \mu _{HM} (\lambda _M - \sigma _{HM} ) \\ + \gamma _{LB} \sigma _{LB} + \gamma _{LM} \sigma _{LM} + \gamma _{HB} \sigma _{HB} + \gamma _{HM} \sigma _{HM} \\ \end{array}$

$\left( {F_B - F_M } \right)\left( {1 + r} \right) - \left( {C_M - C_B } \right) = \left( {\mu _{HB} + \gamma _{LB} + \mu _B } \right) - \left( {\mu _{HM} + \gamma _{LM} + \mu _M } \right) - \left( {F_B - F_M } \right)\mu _R > 0$

$\left( {F_B - F_M } \right)\left( {1 + r} \right) - \left( {C_M - C_B } \right) = \left( {\mu _{LB} + \gamma _{HB} + \mu _B } \right) - \left( {\mu _{LM} + \gamma _{HM} + \mu _M } \right) - \left( {F_B - F_M } \right)\mu _R > 0$

$2\left( {C_M - C_B } \right) - \left( {F_B - F_M } \right)\left( {1 + r} \right) = \left( {\gamma _{LM} + \gamma _{HM} + \mu _M } \right) - \left( {\gamma _{LB} + \gamma _{HB} + \mu _B } \right) + \left( {F_B - F_M } \right)\mu _R > 0$

$\lambda _B^* = \sigma _{HB}^* = \sigma _{LB}^* = \frac{{\left( {\alpha - C_M } \right) + 2(C_M - C_B ) - (F_B - F_M )(1 + r)}}{{(N + 1)\beta }} \\ > \frac{{2(C_M - C_B ) - (F_B - F_M )(1 + r)}}{{(N + 1)\beta }} > 0$

$\lambda _M^* = \sigma _{HM}^* = \frac{{\left( {\varepsilon - F_B (1 + r)} \right) + 2\left\{ {(F_B - F_M )(1 + r) - (C_M - C_B )} \right\}}}{{(N + 1)\beta }} \\ > \frac{{2\left\{ {(F_B - F_M )(1 + r) - (C_M - C_B )} \right\}}}{{(N + 1)\beta }} > 0$

$\lambda _R^* = \Lambda - \lambda _B^* F_B - \lambda _M^* F_M \\ = \Lambda - \frac{{(\alpha - C_M )}}{{(N + 1)\beta }}F_B - \frac{{\left( {\varepsilon - F_M (1 + r)} \right)}}{{(N + 1)\beta }}F_M - \frac{{\left\{ {2(C_M - C_B ) - (F_B - F_M )} \right\}}}{{(N + 1)\beta }}(F_B - F_M )$

This form shows three tables next to each other below the form's title. For simplicity each table will be shown by itself. Row numbers are shown in parenthesis ().

 Participant Number: Market Period:

How many certificates will you buy? (Circle One)

Left-hand: (0) 0 for 0 francs, (1) 1 for 30 francs, (2) 2 for 60 francs (circled), (3) 3 for 90 francs, (4) 4 for 120 francs . . . (15) 15 for 450 francs, (16) 16 for 480 francs

Right-hand: (0) 0 for 0 francs, (1) 1 for 70 francs, (2) 2 for 140 francs, (3) 3 for 210 francs, (4) 4 for 280 francs (circled) . . . (15) 15 for 1050 francs, (16) 16 for 1120 francs

MARKET 1: How many certificates will you redeem in Market 1? (Circle One)

Left-hand: (0) 0 for a fee of 0 francs, (1) 1 for a fee of 50 francs (circled), (2) 2 for a fee of 100 francs, (3) 3 for a fee of 150 francs, (4) 4 for a fee of 200 francs . . . (15) 15 for a fee of 750 francs, (16) 16 for a fee of 800 francs

Right-hand: (0) 0 for a fee of 0 francs, (1) 1 for a fee of 10 francs, (2) 2 for a fee of 20 francs, (3) 3 for a fee of 30 francs, (4) 4 for a fee of 40 francs (circled) . . . (15) 15 for a fee of 150 francs, (16) 16 for a fee of 160 francs

MARKET 2: How many certificates will you redeem in Market 2? (Circle One)

Left-hand: (0) 0 for a fee of 0 francs, (1) 1 for a fee of 50 francs, (2) 2 for a fee of 100 francs (circled), (3) 3 for a fee of 150 francs, (4) 4 for a fee of 200 francs . . . (15) 15 for a fee of 750 francs, (16) 16 for a fee of 800 francs

Right-hand: (0) 0 for a fee of 0 francs, (1) 1 for a fee of 10 francs, (2) 2 for a fee of 20 francs, (3) 3 for a fee of 30 francs (circled), (4) 4 for a fee of 40 francs . . . (15) 15 for a fee of 150 francs, (16) 16 for a fee of 160 francs

This form shows three tables next to each other below the form's title. For simplicity each table will be shown by itself.

 Participant Number: Market Period:

ACCOUNTING SHEET

EXPENSES

Purchases (francs)

Left-hand Certificates_____ Right-hand Certificates_____ Total Purchases (Less than 1001 francs )_____

Redemption Fees (francs)

Market 1: Left-hand Certificates_____ Right-hand Certificates_____ Total Redemption Fees_____
Market 2: Left-hand Certificates_____ Right-hand Certificates_____ Total Redemption Fees_____

Total Purchases (Less than 1001 francs ) + Market 1 Total + Market 2 Total = TOTAL EXPENSES:_____

REVENUE

Number of Certificates Redeemed

Market 1: Left-hand + Right-Hand = Total Number Redeemed x Redemption Values (francs) = Total Income (francs)
Market 2: Left-hand + Right-Hand = Total Number Redeemed x Redemption Values (francs) = Total Income (francs)

TOTAL REVENUE from the REDEMPTION OF CERTIFICATES: Market 1 Total Income (francs) + Market 1 Total Income (francs)

PROFIT from the Redemption of Certificates = REVENUE minus EXPENSES:

Francs not used to purchase certificates x 1.2:

Payoff = PROFIT plus (Unused FRANCS x 1.2):