Get 2x2 game solutions

Get 2x2 Nash equilibrium and first best

get_2x2_game_solutions(payouts, output = "solution")

Arguments

payouts	List of payouts from get_2x2_payouts
output	Either "solution", "NE", "FB", or "dilemma", or "type". See Value section.

Value

The output variable determines the type of output. The options are:

• "solution": a payout tibble is returned that contains additional columns NE and FB columns containing the solution.

• "NE": the pure strategies where NE == 1 or 0.

• "FB": the pure strategies where FB == 1.

• "dilemma": whether the game is a "social dilemma" or "agreement".

• "type": the payout structure for each player.

Details

This function evaluates Nash stability by checking, for each combination of pure strategies, if any player is incentivized to change their strategy. The set of pure strategies can be stable (NE set to 1), neutral (NE set to 0), or unstable (NE set to -1). The first two (0 and 1) represent Nash equilibria. The first best solution is calculated as the set of pure strategies that product the highest net payout among all players (i.e., the sum for all players). A value of 1 indicates the set of pure strategies is a joint optimum, and 0 indicates it is not.

Examples

payouts <- get_2x2_payouts(3, 3, Cs = 2, Cd = 3)
get_2x2_game_solutions(payouts)
#> # A tibble: 4 x 12
#>       A     B    tA    tB  Cs_A  Cs_B  Cd_A  Cd_B    UA    UB    NE    FB
#>   <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1     0     0     3     3     0     0    -3    -3    -3    -3     1     0
#> 2     0     1     3     3     0    -2     0    -3     0    -5    -1     0
#> 3     1     0     3     3    -2     0    -3     0    -5     0    -1     0
#> 4     1     1     3     3    -2    -2     0     0    -2    -2    -1     1

# Note that this function is contained in get_2x2_ggplot, if desired
get_2x2_ggplot(payouts, equilibria = TRUE)
payouts_ii <- get_2x2_payouts(3, 1, Cs = 2, Cd = 3, TRUE)

weights <- c(0.5, 0.5)
weighted_payouts <- get_2x2_weighted_payouts(list(payouts, payouts_ii), weights = weights)
get_2x2_game_solutions(weighted_payouts, "NE")
#> [1] "A0B0"
get_2x2_game_solutions(weighted_payouts, "FB")
#> [1] "A1B0"
get_2x2_game_solutions(weighted_payouts, "type")
#> [1] "Dl-Pd"
get_2x2_game_solutions(weighted_payouts, "dilemma")
#> [1] "social dilemma"