reference/information

wave 2

wave 3

QUESTION 1

A) Using models of oligopoly conduct developed in this course, analyze the possible equilibria of these this Bertrand oligopoly games. What prices should we expect to see if firms are competing? What prices should we expect to see if firms are colluding? In which wave(s) are collusive equilibria possible, and in these is collusion tacit or explicit?

B) Interpret the data from our exercise in view of your predictions above. On what dimensions are your predictions confirmed? Are there dimensions on which your predictions are contradicted? In answering these questions, it is worth thinking about not only the specific equilibrium outcomes predicted, but also the process by why behavior might converge to equilibrium.

In this exercise, you were asked to take on the role of a firm engaged in Bertrand competition against one rival at a time. The simulation unfolded in three waves, with each wave involving several rounds. In each round, two firms were paired on a single market. Both firms could produce the same good (a homogeneous product) at a constant marginal cost MC=2. The firms engaged in Bertrand competition to sell their output to a market with demand described by the demand curve Q=20 - P. Each firm simultaneously announced a price, which could be any multiple of $0.01 between $2 and $20. All consumers then bought from the firm offering the lowest price, which sold the quantity demanded at its price. If the two competing firms announced the same price, they split the quantity demanded at that price. In Wave 1, competing firms were randomly re-paired at the beginning of each round. Thus, each participant would be facing a different competitor in Round 2 than in Round 1, and so on. Results from Wave 1 are described in the following table, which reports average prices, quantities, profits, and consumer surplus across all markets in each round: results.csv In Wave 2, competing firms were paired randomly at the beginning of the exercise. Unlike Wave 1, however, firms were NOT re-paired between rounds. Thus, each player was aware that they faced the same competitor for the whole exercise. The competitor's identity was not, however, revealed. Results from Wave 2 are described in the following figure, which illustrates the evolution of prices, profits, and consumer surplus in each market (pair of firms) over time: ex2 prices by market.pdf ex2 profit by market.pdf ex2 cs by market.pdf Finally, in Wave 3, competing firms were again paired randomly at the beginning of the exercise, with no re-matching over time (so, like Wave 2, each firm knew it was facing the same rival for the whole wave). Unlike Wave 2, however, the identities of competing firms were revealed at the beginning of the game. Each firm thus knew not only that they were facing the same rival over time, but who this rival was. If they chose, competing firms could thus use this information to communicate. Unfortunately, due to time constraints, we were unable to run Wave 3 this semester. Results from a prior semester's Wave 3 are described in the following figures, which illustrates the evolution of prices, profits, and consumer surplus in each market (pair of firms) over time: Round \[ \begin{array}{l} \begin{array}{lllllll} \multicolumn{1}{l}{\mathrm{P}} & \mathrm{Q} & \mathrm{PS} & \text { CS } & \text { askP } & \text { paidP } \\ 1 & 2.996667 & 17.00333 & 16.28663 & 144.8867 & 4.831667 & 2.957849 \end{array} \\ \begin{array}{llllllll} 2 & 2.663333 & 17.33667 & 11.27997 & 150.39 & 3.913333 & 2.650642 \end{array} \\ \begin{array}{llllllll} 3 & 2.253333 & 17.74667 & 4.372467 & 157.5338 & 2.458333 & 2.246382 \end{array} \\ \begin{array}{lrrrrrr} 4 & 2.07 & 17.93 & 1.2533 & 160.7434 & 2.225 & 2.0699 \end{array} \\ \end{array} \] Round Round Round Round Round In this exercise, you were asked to take on the role of a firm engaged in Bertrand competition against one rival at a time. The simulation unfolded in three waves, with each wave involving several rounds. In each round, two firms were paired on a single market. Both firms could produce the same good (a homogeneous product) at a constant marginal cost MC=2. The firms engaged in Bertrand competition to sell their output to a market with demand described by the demand curve Q=20 - P. Each firm simultaneously announced a price, which could be any multiple of $0.01 between $2 and $20. All consumers then bought from the firm offering the lowest price, which sold the quantity demanded at its price. If the two competing firms announced the same price, they split the quantity demanded at that price. In Wave 1, competing firms were randomly re-paired at the beginning of each round. Thus, each participant would be facing a different competitor in Round 2 than in Round 1, and so on. Results from Wave 1 are described in the following table, which reports average prices, quantities, profits, and consumer surplus across all markets in each round: results.csv In Wave 2, competing firms were paired randomly at the beginning of the exercise. Unlike Wave 1, however, firms were NOT re-paired between rounds. Thus, each player was aware that they faced the same competitor for the whole exercise. The competitor's identity was not, however, revealed. Results from Wave 2 are described in the following figure, which illustrates the evolution of prices, profits, and consumer surplus in each market (pair of firms) over time: ex2 prices by market.pdf ex2 profit by market.pdf ex2 cs by market.pdf Finally, in Wave 3, competing firms were again paired randomly at the beginning of the exercise, with no re-matching over time (so, like Wave 2, each firm knew it was facing the same rival for the whole wave). Unlike Wave 2, however, the identities of competing firms were revealed at the beginning of the game. Each firm thus knew not only that they were facing the same rival over time, but who this rival was. If they chose, competing firms could thus use this information to communicate. Unfortunately, due to time constraints, we were unable to run Wave 3 this semester. Results from a prior semester's Wave 3 are described in the following figures, which illustrates the evolution of prices, profits, and consumer surplus in each market (pair of firms) over time: Round \[ \begin{array}{l} \begin{array}{lllllll} \multicolumn{1}{l}{\mathrm{P}} & \mathrm{Q} & \mathrm{PS} & \text { CS } & \text { askP } & \text { paidP } \\ 1 & 2.996667 & 17.00333 & 16.28663 & 144.8867 & 4.831667 & 2.957849 \end{array} \\ \begin{array}{llllllll} 2 & 2.663333 & 17.33667 & 11.27997 & 150.39 & 3.913333 & 2.650642 \end{array} \\ \begin{array}{llllllll} 3 & 2.253333 & 17.74667 & 4.372467 & 157.5338 & 2.458333 & 2.246382 \end{array} \\ \begin{array}{lrrrrrr} 4 & 2.07 & 17.93 & 1.2533 & 160.7434 & 2.225 & 2.0699 \end{array} \\ \end{array} \] Round Round Round Round Round