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Add threshold legend and update setup.py.
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manuelbieri committed Nov 5, 2021
2 parents 04f6992 + 3607cc3 commit f91ad5e
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2 changes: 2 additions & 0 deletions Shelegia_Motta_2021/IModel.py
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Original file line number Diff line number Diff line change
Expand Up @@ -171,6 +171,7 @@ def plot_incumbent_best_answers(self, axis: matplotlib.axes.Axes = None, **kwarg
Optional key word arguments for the best answers plot.<br>
- title: title on top of the plot, instead of the default title.<br>
- options_legend: If true, an additional legend, explaining the options of the entrant and the incumbent, will be added to the plot.<br>
- thresholds_legend: If true, an additional legend explaining the thresholds of the entrant and the incumbent will be added to the plot.<br>
Returns
-------
Expand All @@ -192,6 +193,7 @@ def plot_equilibrium(self, axis: matplotlib.axes.Axes = None, **kwargs) -> matpl
Optional key word arguments for the equilibrium plot.<br>
- title: title on top of the plot, instead of the default title.<br>
- options_legend: If true, an additional legend, explaining the options of the entrant and the incumbent, will be added to the plot.<br>
- thresholds_legend: If true, an additional legend explaining the thresholds of the entrant and the incumbent will be added to the plot.<br>
Returns
-------
Expand Down
115 changes: 85 additions & 30 deletions Shelegia_Motta_2021/Models.py
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Original file line number Diff line number Diff line change
Expand Up @@ -243,8 +243,9 @@ def _plot(self, coordinates: List[List[Tuple[float, float]]], labels: List[str],
axis.add_patch(poly)

axis.legend(bbox_to_anchor=(1.3, 1), loc="upper left")
if kwargs.get('options_legend', False):
axis.text(-0.05, -0.4, self._create_options_legend(), verticalalignment='top')
additional_legend: str = self._create_additional_legend(options_legend=kwargs.get('options_legend', False), thresholds_legend=kwargs.get('thresholds_legend', False))
if additional_legend != "":
axis.text(-0.1, -0.6, additional_legend, verticalalignment='top', linespacing=1)
BaseModel._set_axis_labels(axis, title=kwargs.get('title', ''),
x_label=kwargs.get('xlabel', 'Assets of the entrant'),
y_label=kwargs.get('ylabel', 'Fixed costs of copying for the incumbent'))
Expand All @@ -254,15 +255,18 @@ def _plot(self, coordinates: List[List[Tuple[float, float]]], labels: List[str],
def plot_incumbent_best_answers(self, axis: matplotlib.axes.Axes = None, **kwargs) -> matplotlib.axes.Axes:
poly_coordinates: List[List[Tuple[float, float]]] = self._get_incumbent_best_answer_coordinates()
poly_labels: List[str] = self._get_incumbent_best_answer_labels()
axis: matplotlib.axes.Axes = self._plot(title=kwargs.get("title", "Best Answers of the incumbent to the choices of the entrant"),
coordinates=poly_coordinates, labels=poly_labels, axis=axis, options_legend=kwargs.get('options_legend', False))
axis: matplotlib.axes.Axes = self._plot(
title="Best Answers of the incumbent to the choices of the entrant",
coordinates=poly_coordinates, labels=poly_labels, axis=axis, **kwargs)
return axis

def _create_choice_answer_label(self, entrant: Literal["complement", "substitute", "indifferent"],
incumbent: Literal["copy", "refrain"],
development: Literal["success", "failure"]) -> str:
development: Literal["success", "failure"],
kill_zone: bool = False) -> str:
return self.ENTRANT_CHOICES[entrant] + " $\\rightarrow$ " + self.INCUMBENT_CHOICES[
incumbent] + " $\\rightarrow$ " + self.DEVELOPMENT_OUTCOME[development]
incumbent] + " $\\rightarrow$ " + self.DEVELOPMENT_OUTCOME[development] + (
"\n(Kill Zone)" if kill_zone else "")

def _get_incumbent_best_answer_labels(self) -> List[str]:
"""
Expand Down Expand Up @@ -319,7 +323,8 @@ def _get_incumbent_best_answer_coordinates(self) -> List[List[Tuple[float, float
[(self._assets['A-c'], 0), (x_max, 0), (x_max, self._copying_fixed_costs['F(YY)s']),
(self._assets['A-c'], self._copying_fixed_costs['F(YY)s'])],
# Square 4
[(0, max(self._copying_fixed_costs['F(YN)c'], 0)), (self._assets['A-s'], max(self._copying_fixed_costs['F(YN)c'], 0)),
[(0, max(self._copying_fixed_costs['F(YN)c'], 0)),
(self._assets['A-s'], max(self._copying_fixed_costs['F(YN)c'], 0)),
(self._assets['A-s'], self._copying_fixed_costs['F(YN)s']), (0, self._copying_fixed_costs['F(YN)s'])],
# Square 5
[(self._assets['A-c'], self._copying_fixed_costs['F(YY)s']), (x_max, self._copying_fixed_costs['F(YY)s']),
Expand All @@ -334,8 +339,9 @@ def _get_incumbent_best_answer_coordinates(self) -> List[List[Tuple[float, float
def plot_equilibrium(self, axis: matplotlib.axes.Axes = None, **kwargs) -> matplotlib.axes.Axes:
poly_coordinates: List[List[Tuple[float, float]]] = self._get_equilibrium_coordinates()
poly_labels: List[str] = self._get_equilibrium_labels()
axis: matplotlib.axes.Axes = self._plot(title=kwargs.get("title", "Equilibrium Path"),
coordinates=poly_coordinates, labels=poly_labels, axis=axis, options_legend=kwargs.get('options_legend', False))
axis: matplotlib.axes.Axes = self._plot(title="Equilibrium Path", coordinates=poly_coordinates,
labels=poly_labels,
axis=axis, **kwargs)
return axis

def _get_equilibrium_labels(self) -> List[str]:
Expand All @@ -354,7 +360,8 @@ def _get_equilibrium_labels(self) -> List[str]:
# Square 2
self._create_choice_answer_label(entrant="substitute", incumbent="copy", development="success"),
# Square 3
self._create_choice_answer_label(entrant="complement", incumbent="refrain", development="success"),
self._create_choice_answer_label(entrant="complement", incumbent="refrain", development="success",
kill_zone=True),
# Square 4
self._create_choice_answer_label(entrant="substitute", incumbent="refrain", development="success")
]
Expand Down Expand Up @@ -565,18 +572,55 @@ def _draw_vertical_line_with_label(self, axis: matplotlib.axes.Axes, x: float, l
if label is not None:
axis.text(x, label_y, label)

def _create_additional_legend(self, options_legend: bool, thresholds_legend: bool) -> str:
legend: str = ""
if options_legend:
legend += self._create_options_legend()
if thresholds_legend:
legend += self._create_thresholds_legend()
return legend

def _create_options_legend(self, latex: bool = True) -> str:
space: str = "$\quad$" if latex else "\t"
return "Options of the entrant:\n" + \
space + self.ENTRANT_CHOICES['complement'] + ": Tries to develop an additional complementary product to a primary product.\n" + \
space + self.ENTRANT_CHOICES['substitute'] + ": Tries to develop an substitute to the primary product of the incumbent.\n" + \
space + self.ENTRANT_CHOICES['indifferent'] + " : Indifferent between the options mentioned above.\n" + \
"Options of the incumbent:\n" + \
space + self.INCUMBENT_CHOICES['copy'] + " : Tries to develop an additional complementary product to a primary product.\n" + \
space + self.INCUMBENT_CHOICES['refrain'] + " : Tries to develop an additional complementary product to a primary product.\n" + \
"Outcomes of the development:\n" + \
space + self.DEVELOPMENT_OUTCOME['success'] + " : The additional product can be developed, since the entrant has sufficient assets.\n" + \
space + self.DEVELOPMENT_OUTCOME['failure'] + " : The additional product can not be developed, since the entrant has not enough assets."
space + self.ENTRANT_CHOICES[
'complement'] + ": Develop an additional complementary product to a primary product.\n" + \
space + self.ENTRANT_CHOICES[
'substitute'] + ": Develop an substitute to the primary product of the incumbent.\n" + \
space + self.ENTRANT_CHOICES['indifferent'] + " : Indifferent between the options mentioned above.\n" + \
"Options of the incumbent:\n" + \
space + self.INCUMBENT_CHOICES[
'copy'] + " : Copy the original complement of the entrant.\n" + \
space + self.INCUMBENT_CHOICES[
'refrain'] + " : Do not copy the original complement of the entrant.\n" + \
"Outcomes of the development:\n" + \
space + self.DEVELOPMENT_OUTCOME[
'success'] + " : The entrant has sufficient assets to develop the product.\n" + \
space + self.DEVELOPMENT_OUTCOME[
'failure'] + " : The entrant has not sufficient assets to develop the product."

@staticmethod
def _create_thresholds_legend() -> str:
space: str = "$\quad$"
return "Thresholds for the assets of the entrant:\n" + \
space + r'$\bar{A}_S$' + ": Minimum level of assets to ensure a perfect substitute\n" + \
space + space + space + " gets funded if the incumbent copies.\n" + \
space + r'$\bar{A}_C$' + ": Minimum level of assets to ensure another complement\n" + \
space + space + space + " gets funded if the incumbent copies.\n" + \
"If the incumbent does not copy, the entrant will have sufficient assets.\n\n" + \
"Thresholds for the fixed costs of copying for the incumbent:\n" + \
space + r'$F^{YY}_S$' + ": Maximum costs of copying that ensure that the incumbent\n" + \
space + space + space + space + "copies the entrant if the entrant is guaranteed to invest\n" + \
space + space + space + space + "in a perfect substitute.\n" + \
space + r'$F^{YN}_S$' + ": Maximum costs of copying that ensure that the incumbent\n" + \
space + space + space + space + "copies the entrant if the copying prevents the entrant\n" + \
space + space + space + space + " from developing a perfect substitute.\n" + \
space + r'$F^{YY}_C$' + ": Maximum costs of copying that ensure that the incumbent\n" + \
space + space + space + space + "copies the entrant if the entrant is guaranteed to invest\n" + \
space + space + space + space + "in another complement.\n" + \
space + r'$F^{YN}_C$' + ": Maximum costs of copying that ensure that the incumbent\n" + \
space + space + space + space + "copies the entrant if the copying prevents the entrant\n" + \
space + space + space + space + "from developing another complement.\n"

@staticmethod
def _get_color(i: int) -> str:
Expand Down Expand Up @@ -658,6 +702,7 @@ class BargainingPowerModel(BaseModel):
Besides the parameters used in the paper, this class will introduce the parameter $\\beta$ in the models, called
the bargaining power of the incumbent. In the paper the default value 0.5 is used to derive the results.
"""

def __init__(self, u: float = 1, B: float = 0.5, small_delta: float = 0.5, delta: float = 0.51,
K: float = 0.2, beta: float = 0.5):
"""
Expand Down Expand Up @@ -796,10 +841,13 @@ def get_payoffs(self) -> Dict[str, Dict[str, float]]:
return self._payoffs

def _get_incumbent_best_answer_coordinates(self) -> List[List[Tuple[float, float]]]:
coordinates: List[List[Tuple[float, float]]] = super(BargainingPowerModel, self)._get_incumbent_best_answer_coordinates()
coordinates: List[List[Tuple[float, float]]] = super(BargainingPowerModel,
self)._get_incumbent_best_answer_coordinates()
if self._copying_fixed_costs["F(YY)s"] != self._copying_fixed_costs["F(YN)c"]:
coordinates.append([(self._assets['A-s'], self._copying_fixed_costs['F(YY)s']), (self._assets['A-c'], self._copying_fixed_costs['F(YY)s']),
(self._assets['A-c'], max(self._copying_fixed_costs['F(YN)c'], 0)), (self._assets['A-s'], max(self._copying_fixed_costs['F(YN)c'], 0))])
coordinates.append([(self._assets['A-s'], self._copying_fixed_costs['F(YY)s']),
(self._assets['A-c'], self._copying_fixed_costs['F(YY)s']),
(self._assets['A-c'], max(self._copying_fixed_costs['F(YN)c'], 0)),
(self._assets['A-s'], max(self._copying_fixed_costs['F(YN)c'], 0))])
return coordinates

def _get_incumbent_best_answer_labels(self) -> List[str]:
Expand All @@ -808,13 +856,15 @@ def _get_incumbent_best_answer_labels(self) -> List[str]:
if self._copying_fixed_costs["F(YY)s"] > self._copying_fixed_costs["F(YN)c"]:
labels.append(
# Square 7
self._create_choice_answer_label(entrant="substitute", incumbent="copy", development="success") + " \n" +
self._create_choice_answer_label(entrant="substitute", incumbent="copy",
development="success") + " \n" +
self._create_choice_answer_label(entrant="complement", incumbent="refrain", development="success"),
)
else:
labels.append(
# Square 7
self._create_choice_answer_label(entrant="substitute", incumbent="refrain", development="success") + " \n" +
self._create_choice_answer_label(entrant="substitute", incumbent="refrain",
development="success") + " \n" +
self._create_choice_answer_label(entrant="complement", incumbent="copy", development="failure"),
)
return labels
Expand All @@ -824,6 +874,7 @@ class UnobservableModel(BargainingPowerModel):
"""
This model indicates that if the incumbent were not able to observe the entrant at the moment of choosing, the “kill zone” effect whereby the entrant stays away from the substitute in order to avoid being copied) would not take place. Intuitively, in the game as we studied it so far, the only reason why the entrant is choosing a trajectory leading to another complement is that it anticipates that if it chose one leading to a substitute, the incumbent would copy, making it an inefficient strategy for entering the market. However, if the incumbent cannot observe the entrant’s choice of strategy, the entrant could not hope to strategically affect the decision of the incumbent. This would lead to the entrant having a host of new opportunities when entering the market and it makes competing with a large company much more attractive.
"""

def __init__(self, u: float = 1, B: float = 0.5, small_delta: float = 0.5, delta: float = 0.51,
K: float = 0.2, beta: float = 0.5):
"""
Expand All @@ -836,7 +887,8 @@ def plot_incumbent_best_answers(self, axis: matplotlib.axes.Axes = None, **kwarg

def _create_choice_answer_label(self, entrant: Literal["complement", "substitute", "indifferent"],
incumbent: Literal["copy", "refrain"],
development: Literal["success", "failure"]) -> str:
development: Literal["success", "failure"],
kill_zone: bool = False) -> str:
return "{" + self.ENTRANT_CHOICES[entrant] + ", " + self.INCUMBENT_CHOICES[incumbent] + "} $\\rightarrow$ " + \
self.DEVELOPMENT_OUTCOME[development]

Expand Down Expand Up @@ -865,14 +917,16 @@ def get_optimal_choice(self, A: float, F: float) -> Dict[str, str]:
result: Dict = super().get_optimal_choice(A, F)
# adjust the different choices in area three -> since the kill zone does not exist in this model.
if result["entrant"] == self.ENTRANT_CHOICES["complement"]:
result = {"entrant": self.ENTRANT_CHOICES["substitute"], "incumbent": self.INCUMBENT_CHOICES["copy"], "development": self.DEVELOPMENT_OUTCOME["failure"]}
result = {"entrant": self.ENTRANT_CHOICES["substitute"], "incumbent": self.INCUMBENT_CHOICES["copy"],
"development": self.DEVELOPMENT_OUTCOME["failure"]}
return result


class AcquisitionModel(BargainingPowerModel):
"""
In order to explore how acquisitions may modify the entrant’s and the incumbent’s strategic choices, we extend the base model in order to allow an acquisition to take place after the incumbent commits to copying the entrant’s original complementary product (between t=1 and t=2, see table 2). We assume that the incumbent and the entrant share the gains (if any) attained from the acquisition equally.
"""

def __init__(self, u: float = 1, B: float = 0.5, small_delta: float = 0.5, delta: float = 0.51,
K: float = 0.2) -> None:
"""
Expand All @@ -885,8 +939,9 @@ def __init__(self, u: float = 1, B: float = 0.5, small_delta: float = 0.5, delta

def _calculate_copying_fixed_costs_values(self) -> Dict[str, float]:
copying_fixed_costs_values: Dict[str, float] = super()._calculate_copying_fixed_costs_values()
copying_fixed_costs_values.update({'F(ACQ)s': (self._u + self._delta - self._K) / 2 + self._small_delta * (2 - self._beta),
'F(ACQ)c': self._small_delta * (2.5 - 3*self._beta) - self._K / 2})
copying_fixed_costs_values.update(
{'F(ACQ)s': (self._u + self._delta - self._K) / 2 + self._small_delta * (2 - self._beta),
'F(ACQ)c': self._small_delta * (2.5 - 3 * self._beta) - self._K / 2})
return copying_fixed_costs_values

def get_copying_fixed_costs_values(self) -> Dict[str, float]:
Expand All @@ -909,8 +964,8 @@ def get_copying_fixed_costs_values(self) -> Dict[str, float]:


if __name__ == '__main__':
bargaining_power_model = Shelegia_Motta_2021.BargainingPowerModel(beta=0.8)
bargaining_power_model = Shelegia_Motta_2021.BargainingPowerModel(beta=0.6)
fig, (axis_eq, axis_best) = plt.subplots(ncols=2, figsize=(14, 9))
bargaining_power_model.plot_equilibrium(axis=axis_eq, options_legend=True)
bargaining_power_model.plot_incumbent_best_answers(axis=axis_best)
bargaining_power_model.plot_incumbent_best_answers(axis=axis_best, thresholds_legend=True)
plt.show()
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