Question

Suppose there are only two TV stations in Arecima, each broadcasting programming over the airwaves. Each station wishes to get the maximum number of viewers and each is considering whether to carry a reality-tv show or a comedy show in its 11pm slot on Saturdays. The 1000 Arecima residents have the following preferences: 800 of them wish to watch a reality-tv show and have no interest in a comedy show whereas 200 people would enjoy watching a comedy on TV but would go sleep if both stations chose to broadcast a reality tv show. Each station will receive half the audience if both broadcast the same type of show. Write down the `outcome matrix' of this game and find the Nash equilibrium. Is the equilibrium efficient? As usual, justify your answers.

Answer 1

The most efficient option is when one channel telecast reality show and the other broadcasts comedy hence the need of the entire population of 1000 of Arecima will be satisfied. But the channels will not opt for such a situation as the channel which broadcasts comedy will have only 200 viewers while the other channel which broadcast reality show will have 800 viewers. No channel would want be the one telecasting comedy while the other channel broadcasts reality show in spite of such a situation generating maximum benefit since its satisfy the needs of the entire population of Arecima. Hence the channels will settle in telecasting Reality shows in order to maximize their individual benefits. And this causes the 200 comedy viewers in not meeting their need and going to bed their need is not met and 200 viewers loss to the channels. Hence both the channels will broadcasts reality shows thus having splitting the audience of 800 into halves and having 400 viewers each while the 200 citizens who prefer comedy will not be viewing any channel as no channel broadcasts comedy. No nash equlibrium of 400/400 is not efficient as the needs of 200 viewers are not met resulting in not achieving the maximum overall benefit and a loss of 200 viewers to the channels.