check_game_dynamics: Check game dynamics (NOT WORKING)
In gopalpenny/genevoisgame: Genevois Game

Description Usage Arguments Details Value Examples

Check the basic game dynamics, particularly in cases where zRange=0 and the first best and nash outcomes are the same.

1	check_game_dynamics(params, text_results = TRUE, aquifer_type = NULL)

`params`	game parameters
`text_results`	logical value determining if results are returned as text or a tibble
`aquifer_type`	"confined" or "unconfined", or `NULL` – in which case `check_params` will determine the type

In a number of situations, the genevois game does nothing interesting: both players pump at their entire demand, the first best is equivalent to the nash equilibrium, and there are no advantages or disadvantages to signing a treaty. This function helps us better understand why this is the case.

For any interesting dynamics to arise from the game, the First Best has to be different (better) than the Nash Equilibrium. This occurs when players forgo pumping and supply their water from another source, which can only occur if the other source is less expensive than pumping. In other words, pumping for at least one of the players has to be great enough that the cost of pumping is greater than the cost of alternative supply. If this is not the case, then the players cannot do any better working together than they could on their own.

Either (1) a text description of the dynamics (if text_results==TRUE) or (2) a table containing the following values:

: ds_max, df_max: The maximum depth for each player, if both players pump at their demand (Qs, Qf).
: ds_threshold, df_threshold: The depth for each player where the cost of pumping equals the cost of alternative supply (Qi=B*di).

## Not run: 
library(magrittr)

# Table output
check_game_dynamics(example_params_unconfined,text_results = FALSE)
example_params_unconfined %>% dplyr::mutate(Qs=1,Qf=1) %>% check_game_dynamics(text_results = FALSE)

# Text output
check_game_dynamics(example_params_unconfined) %>% cat()
example_params_unconfined %>% dplyr::mutate(Qs=1,Qf=1) %>% check_game_dynamics() %>% cat()

## End(Not run)